The year I don't see his grave, that's the year I become blind. The arba'een that I'm not there, rest assured that's the day I've died. The year I don't see his grave is the year I become blind. The arba'een that I'm not there, rest assured that's the day I've died. Be it that I'm full of youth or that I'm frail and old, his shrine gives me wolf. Without it I'm frail and cold. God forgive me if on judgment day I am asked when I'm cold, you missed arba'een once of its greatness, weren't you told? God forgive me if on judgment day I am asked when I am cold, you missed arba'een once of its greatness, aren't you told? When you told when I'm cold for questioning with dust in my hair I'll come, holding the flag that I held when I walked to Ali's son. Whatever I lost in life on that walk so much more I'd find. The arba'een that I'm not there, rest assured that's the day I've died. I smelled the dust of my heaven walking on that road. The dust that rose traveled with me to heaven's abode. Perhaps it's because the flood of the ark of Noah here once flowed and upon it Hussain the ship of salvation had rode. I see waves float to his grave. I see waves float to his grave. Waves of souls and of people and I see him take him and I see him take them all with him when his ship would set sail. The people he took with him on the road to him have died. The arba'een that I'm not there, rest assured that I've died. It was once upon this road that they walked as captives. It was once upon this road that they walked as captives. Yet alongside her daughters know that Zaynab still lives. I see that flags into our hands, Ruqayah's hand gives. I see that flags into our hands, Ruqayah's hand gives. And the walk of the queen of Hashem every walker relives. But remember as we walk and as in our eyes trickle tears. Remember as we walk and as in our eyes trickle tears. We all walk by Mawakib. Zaynab walked by heads on spears. The stars that sit in the sky with Mawakib are aligned. The arba'een that I'm not there rest assured is that I've died. Yes, yes, yes, we walk yearly on this road the walk of the free. But would we return if impossible it would be? Recall those who were executed for walking on this way. Recall those who were executed for walking on this way. Those who when they reached Hussain's grave for their lives they prayed. O Allah, make me of those when by Hussain's grave they would stand. Had no left hand to be cut so had offered their right hand. When presented with their deaths for Hussain they prayed they gladly signed. The walk to heaven is reserved for the courageous. The walk to heaven is reserved for the courageous. Every step is a Hajj and Umrah. Every step is a step on ISIS. When I see my flag flutter I see fall terrorists. Those blessed to walk this road are reserved for greatness.  No, I am not arrogant but I know well of my worth. Those that try to kill us on that road cannot be of a pure birth. I saw those who know of God leave their work and home behind. The Arba'im that I'm not there rest assured is the day I've died. Those who visit believe in God and God alone. As narration say it's like visiting Allah on his throne. The believers cry as on his grave themselves they've thrown peace be upon that flesh that still remains on those bones. As we hold onto those bars and wonder what is heaven. If it's not if it's not here whilst we're saluting the last of Ali's children we thank Allah for we are the luckiest of mankind. The Arba'im that I'm not there rest assured is the day I've died. The day I die and my body is placed into the ground in the stress of yearning Hussain's grave my head I'll pound. Me the day I die and the day my body is placed into that ground in the stress of yearning Hussain's grave my head I will pound. But no if anyone misses me to return I'll be bound. Every Arba'im on that walk my soul shall be found. Every Arba'im on that walk my soul shall be found. Take a look at those walking you'll find me still amongst them or you'll find me at the end in Hussain's shrine doing Martin and if any need the prayer just ask my grave. I won't mind the Arba'im that I'm not there rest assured is the day I've died.


I think at the end at the end I'm going to do much more of 2d than 3d but I think maybe that's that's already good. So let me spend again like maybe five minutes to give another small exercise. Unfortunately I'm not going through the exercises but for students who they can still see me this week or next week if they want to we can discuss the exercises I gave. So yesterday if you remember I ended up with talking about the problem of this type. I mean we start we looked at an equation of like this and I explained that the main growth was coming from high frequencies here and low frequencies here and then I went through like some reductions to get to some sort of ODE system that mimic what is the maximum growth of this ODE of this equation. And I wanted to explain at least for those who want to do the calculation how you get really the jovree like what will be really the simple ODE systems you have to solve to see the growth. So that's what I want to explain now very rapidly. I mean if you remember I did I said okay let me look at high high low and then you write this as a convolution and at some we ended up with so I go a little bit fast but it's more or less the calculation we did I did a little bit last time maybe giving slightly more. So I wrote something of this type L t square f hat of c and this comes from the low frequency let me not write down precisely what that is. So I said okay this this will be a good candidate to mimic the growth and I'll be putting absolute values everywhere. The first thing I explained is to remove this replace this like also by one replace this by eta so this was the first thing we did okay put absolute values think about there there are absolute values everywhere and then I said only the modes k less than square root of eta these are the modes that are important but then you look here and you start seeing that it's really if you think about this as being time and I explained this I think last time it's if I write k zero to be like square root of eta at each I mean if you look at times between square root of eta and eta so I'm only looking at times here I mean that's where that's where this denominator can start having problems actually so the whole I mean I have to spend some time looking at this ODE and see what is really the path where you can have the maximum growth and try to estimate it and it turns out that path is more or less the following one let me put I mean at the beginning the times are much more closer very close to each other but at later time they they get I mean here close to square root of eta there are many many resonances at later time there are more spread basically okay so the worst the worst actually scenario is when the mode is the following is the mode k zero talks to the mode k zero minus one talks to the mode k zero minus two till you get to talking to the mode one right because that's where you will be getting the maximum growth at each time this was already like in the paper of or of 07 1907 he more or less says something about that sort of transient growth I mean all these pictures related to that transient growth and he mentions that okay he mentioned in his paper that it's possible that this transient growth gives problems because of like transient growth I mean the idea here is exactly the fact that you see like the mode let's say the mode k zero will grow at this time but then at this time it can talk to the mode k zero minus one and the mode k zero minus one will grow later right that's more or less so the mode k zero will talk to the mode k zero minus one and the mode k zero minus one grows later and so on so that's really more or less the the sort of possible cascade that happen it is it is not it is like a non-linear effect because there is this term that may remove I mean there should be some low frequency there that makes this energy cascade possible okay so it is a non-linear effect okay so now how how can we how can we get to exactly that exponential of square root of eta the way you do it is so you split these intervals so there will be at I split this the whole thing into small intervals centered that around these numbers and on each one of these intervals I will solve some sort of ODE that I mean like that may make that may make the the maximum growth basically it's not a difficult I mean like the the ODE one can solve it I mean it's very simple it's not difficult so what what is this so FR will be will correspond to the mode k in which you are here let's say you are in this interval FR if you are in that interval FR will be fk0 minus 2 if you are in this interval right and f and r will correspond to all the other modes and you can say okay this is what is the growth that this system of ODE can encounter along this interval okay so you you plug in you do some calculations and you end up and I leave this as an exercise for those who want to do it you end up here with exactly the growth that you get is eta over k square to some small power okay the small power is related to kappa the kappa here is related to the smallness of my data so the kappa is related to the size of this guy I mean this guy has think of this as small it's of size kappa okay so it's not difficult like you take this as a system and you try to solve it between actually between times let's say okay I'll make a change of variable I replace this by tau now if I replace this by tau okay now I'm going to replace t I'm going to write tau equal t minus eta over k and then this becomes one plus tau square okay so then you look at this ODE and you look at it for tau in the interval minus eta over k square eta over k square that correspond exactly to this interval here okay and then you you assume that your f r and f n r are of size one at this time you run this and you want to see how large they become at this time it turns out interestingly enough very interesting thing happens that they first of all first of all this guy grows faster in the first part of the interval and in the second part this catches up and it turns out at the end they they grow exactly of similar way and they grow exactly of of this amount okay I mean simple exercise just just ODE so then okay you put all this growth together so you put all this growth together so starting from the growth coming from k zero remember k zero was this and then you continue till you get to one to the power c okay so it's the product product of all these numbers then you use your sterling formula and you see that this is exponential some constant related to the constant you have here square root of eta so using sterling formula so let me leave this as exercise so there are two parts in the exercise first of all you look at this ODE and you try to find out that this is the growth that you get and then you put all these growth together and you see that it is some exponential square root of eta so then it means that if you I mean if you if you think that this sort of growth is possible in your equation it means that you have really to be assuming jeuvre regularity and I think we have we are almost now confident that it's possible to get this growth right you can you can cook up some way of taking your data so that you see this growth okay so let me now state a theorem at least I can state a theorem and then maybe I'll say two words about proofs but but then I want to talk more about the 3d case maybe insist more on differences so what is what would be the theorem so the theorem so this is a theorem with I forgot the year I think the public published last year that was the publication so we start with s here and we take some lambda 0 lambda prime so this will be I mean s will be fixed this is like the amount like as the radius of analyticity that you have initially and this is what you get at the at the final time so then there exists an epsilon 0 such that for all epsilon less than epsilon 0 if your omega initial so omega initial is a function of x and y satisfies so I think there was any question about it like the the integral dx d omega this is 0 I mean it's always you can always take that to be 0 and there is a reason I mean that I got the question about it so I think you can remember why we need that we need also some sort of what this is less than yeah less than epsilon or so so you need like some weight but just one weight will be enough and your omega initial in the jeuvre lambda 0 I mean the jeuvre of class 1 over s but with the radius lambda 0 let me recall what this is this will be the sum of a k the integral omega initial hat k eta to the power s I put a 2 here because I'm squaring things d eta so here I'm integrating in eta summing in k and this is the weight I'm putting okay s s is strictly bigger than one half so remember because this is the possible growth I'm I may be getting from this sort of toy model so at the end of the day I will still keep a little bit of of this okay yes I demand that this is less than epsilon square so then the conclusion is what so these are the assumptions on my initial data then there exists some f infinity of x y yeah I mean I think it's better that you I write it as capital X because yes okay so the integral of this f infinity is also 0 but now the f infinity in the lambda prime norm is now instead of being less than epsilon it will be less than some 10 epsilon maybe okay so around to grow a little bit but you see I'm not allowing it to grow too much but I'm losing regularity so again I mean the point here is that all this growth that you see here instead of seeing it as time growth there I'm seeing it as loss of regularity so that's I think that's really the main thing and then the conclusion is that my my omega so my vorticity will be converging to this f infinity so that will be my final profile in a sense but then I have to I have to make to write down the right change of variable so x remember like if you remember the x was my x minus ty in the linear case but then in the non-linear case I added some other stuff but then I see how I'm going to write down this my omega omega is a function of small x so then I have to write down the small x as function of capital X plus ty plus all those other partial things so that's why it's written this way plus some phi of ty this is coming from the non-linear term y minus f infinity of capital X y in the jeuvre norm this will be decaying like epsilon square over t okay I mean here somehow I I mean the statement I'm writing it in terms of the original omega but the proof is really done with what what I think last time I called f f was written in the new coordinate system so basically the the way the proof goes is really that you prove that your f converges to this okay and phi phi of ty is is really the piece that was here yesterday right so it's it's really the non-linear the non-linear part of the change of variable so it's somehow something like this um the integral between zero and t and then it is the the zero mode of the u1 which was a function of s and y ds okay and actually one can prove that this is equal to some u infinity of y t plus some b o of epsilon square okay um the u infinity the u infinity of y is the velocity the first component of the velocity related to this guy so um let me finish writing the result here so u infinity of y is like dy and then it's dy y minus one so of course then it becomes dy minus one of the integral of f infinity of x y dx okay so it's really the velocity associated I mean if you think of this as your vorticity um what will be the first component of the the first component of the velocity which is the zero mode the zero mode of the first component of the velocity okay um so that's that's really the main statement about the convergence of the vorticity and then okay I mean there are other statements about um the decay of the of the velocity really um so then I mean these are not very difficult to get I mean that's really the main part of the proof that the the rest comes for free so now if I take this minus u infinity of y so it's really like the error between this and the limit guy so I think I mentioned this last time normally in in problems like this you expect this to be one over t right usually but it turns out here it's one over t square there is some subtle some subtle cancellations that okay I mean like and it's really the reason why this is t and then constant is no log term there's a no log term I mean the first version of the paper we had to log there but okay we were we observed that there is some sort of nice cancellation that makes this one over t square but that's really for the zero mode so the zero mode converges faster than maybe what you expect okay I mean this is again I mean think of this as a function of t and y okay and then the non-zero modes the non-zero modes if I write down if you remember I used this notation for the non-zero modes I mean this happens in Juvre the non-zero modes if I write them down in the original variable okay I'm mixing variables but if I write down the things in the original variables for the non-zero modes I can only get convergence in L2 I will not get convergence in high space because like derivative will cost me t of course if you write them down in the rescaled in the in this coordinate in the capital X coordinate you get convergence in Juvre okay but that's I think I don't want to insist on these things because that's not really how the main part of the proof goes okay so that's more or less what will be a statement I think you can ignore these parts of the statements but just remember this part yes yes here zero I don't know you said the non-zero the zero mode yeah yeah okay I mean I wrote the integral so I wrote the average here so but I think I can if I if I am if I no no but I think it's better I mean if I am if I am more I will use this notation I mean that that would be the better way of writing so then yes yeah yeah so right yes the integral yes so the integral is exactly like to avoid to avoid when you invert the Laplacian when k is when k is zero when you invert the Laplacian so it's it's really inverting this guy so then you don't want when you invert this you want you don't want to be dealing with low frequencies and so on so it's just problem of low frequencies in y and also the second one is is is also the condition so both are really for which I think I mean like in the Navier stocks community it's always whenever you are in the torus it's it's really the the natural assumption that you make like you have average zero I think you can even recover I mean if you just take yeah I mean like if you take the velocity you take that the vorticity is the gradient of the velocity then you'll have it yeah I mean it is it is I mean otherwise you are in energy not infinite energy right so f infinity basically norm I mean here it is like a perturbative result so basically like your f infinity is like equal to your omega initial plus big o of epsilon square so it's like scatter I mean it's like in scattering theory like no no I took the translation out I mean this is taking the translation out right so I mean I think one can think of this I mean it has a lot of similarity with scattering but of course like it's it's not just I mean the linear thing you have to filter with depends on your final thing I mean that's one another difficulty also in the proof like you don't know this state initially so but then you filter with this and then you prove that this behaves like that at the end right but of course you can write a form I mean you can write an infinite integral to to write down what is this right it's possible okay so this is the statement um I'm not going to talk about proof because otherwise I mean I will not have time to talk about the 2d the 3d but let me just mention one thing since I thought I told you a little bit about this toy model and so on it's so I mean in all the in proofs whenever people use proofs using these jewelry norms the typical the way usually these proofs work is that you will you will try you will try to um you will try to um so as I said like f I explained what was f last time f is after I apply the change of variable so my f my f of t x v I mean yesterday I also introduced v but in the statement you don't need the v is my omega of t x y I'm not going to recall the change of variable just so usually proofs um in analytic or jewelry regularity at least um will try to estimate f of t in some lambda of t right and you will allow your lambda of t to to go from um from your lambda zero to your lambda prime right and this is really what is behind the idea of Koshy Kowalewski like when time goes you your radius of analyticity let's say decays and I think I think this type of norms in the fluid community was used by first I think the moment voyage like the paper of end of the 70s they they use this type of norms but they used it for in the analytic case okay it turns out that I mean this was our first guess I mean let's try to use norms like that that's not enough that's not enough because this will be losing the jewelry regularity for all frequency in the same way however if you remember this toy model like for the frequency eta the loss of regularity happens exactly in this interval right so we cannot we cannot use this let's say democratic way of losing regularity for everyone the same time so each one will be losing each frequency loses its regularity at a particular time so that's why we need a much more complicated norm that that actually uses a lot this toy model so it is based on the toy model precisely you mean that you have a weight function which depends on eta in a more complicated way exactly exactly exactly I mean I can write it down but I think I think I get I think I will not do it because I mean you get the idea basically like we will write a weight function that mimic this growth of the ODE and we will put it here as a weight in front right it is a little bit also in the spirit of this I always mentioned like Alina like this ghost the ghost energy of Alina it is in that spirit also I think okay so any questions about this 2d case on otherwise I'll move to the 3d okay yeah I think I said more or less what I wanted to say about this okay now 2d so let's let's go again back to simpler thing or 3d so let's go back to some simple things and what I want to insist upon is differences more than doing the the 3d precisely oh let me leave this because this is part yeah so I mentioned that this was the result with Jacob and then we had another result with also in collaboration with V call where we extend this to the case where we put a viscosity of course in this proof with with we call the viscosity didn't help us at all like we had really more I mean the proof was more to just make sure that the viscosity doesn't come and destroy all the nice properties we had here and one of the other things about it is the fact that at the end of the day we have to go back to quit like this will go to zero basically because in in the in the I mean there is a visc there is a viscosity that will kill this guy also okay so now 3d okay so I'm not going to rewrite the the equation I wrote about you I'm more or less going to assume that you you have it or maybe I should rewrite it okay let's assume that you remember it or maybe I can write down the equation that was so I had the V which I wrote something like this plus U and then U is the small perturbation and I can write down an equation on this small u equal minus u 2 0 0 so I will try also to go to follow the same the same way that I talked about the 2d and mention first like linear effects and then try to talk a little bit about non-linear effects so what is the first linear effect the first linear effect is to say okay let's let's try to get rid of this large transporter and then the change of variable the natural change of variable is the same as the same as in 2d so at the linear level it is the same the change of variable the natural change of variable is the same and if you do that okay so right so here I'm working with with the velocity equation rather than the vorticity that's a big difference there I mean like you can try to write down the vorticity here but it's not useful at all so right so I'm going to use the notation capital U capital U in these variables is the small u in these variables so then I can write an equation on this capital U and then I get the following equation of course now capital U is not um capital U is is not necessary divergence free but it is it is divergence free you know I mean it is this divergence which is free okay and I recall which I explained last time this is what this is dx dy minus t dx dz and this Laplacian is just um the gradient l square okay so few observations here um okay I kept the non-linear term even though this is I call this like a linear change of variable of course there will be another non-linear change of variable to take into account this guy but if you remember last time when I wrote the equation on the vorticity when I wrote the equation on the vorticity there was a nice property is that there was some if you remember there was some nice cancellation and here I didn't have this gradient l it was just a gradient this is a one one difficulty that comes in 3d that we didn't have in 2d the fact I mean remember that you want the non-linear term to be the smallest possible so that it doesn't perturb your linear dynamic so that was one observation okay so so the p we have here I mean we can compute it actually explicitly I mean you can write down an equation about it so it's I mean you can take the divergence you can take this divergence term like this will disappear and um actually the pressure as I wrote it here the pressure has two pieces into it so there is a linear part of the pressure p l and p n l you can you can observe that you have two pieces in the pressure it's a simple calculation let me do okay now I want to I want to look at the if you remember last like when we talked about the 2d there was two important linear effect inviscid dumping and enhanced dissipation right so remember those two um so inviscid dumping is the decay that comes without the viscosity help okay and um and then enhanced dissipation was the decay that comes with the viscosity but it is enhanced by the help of by the help of the of the shearing in a sense um okay here here it's not clear um what what is the how how we can do inviscid dumping here so so so let me let me for now forget about the non-linear term let me for now forget about the non-linear term okay so just explain the difficulty that comes from the change of variable about it but just now think about this equation so there is it turns out that there is a good quantity that replaces the vorticity there's one good quantity that replaces the vorticity which is so called q2 I mean q q2 which is Laplacian l of u2 okay I mean you can also write it down in the original variable in the original variable it is just the Laplacian of u2 right in original variable it is q2 equal Laplacian of u2 and um I mean this goes back actually to Kelvin Kelvin already already noticed that this was a good quantity actually the enhanced dissipation I mentioned last time the calculation like that sort of decay mu to the minus one-third was already computed by Kelvin if you go you read the paper of Kelvin you see that calculation precisely so uh there's this nice cancellation that happens basically I mean it's not it's not like something you can see immediately why that's a good that's a good guy but you you do the calculation I mean you can do it you have the choice you can do it on the original variable or the or the second one and what you end up with at the at the linear level you end up with the following equation dt q2 equal new Laplacian l of q2 that's very good right I mean it's some nice cancellation happening and so on and then you you get that I mean if you write it if you write it on small q2 if you write it with the small q2 you will get the same but with Laplacian small q2 I mean you have to do the calculation to believe that it is correct but somehow there is a cancellation between these two guys basically there's some sort of some sort of cancellation between actually this and the linear part of the pressure right so you you see like the pressure has I mean you can compute it even though I didn't write it down but okay let me I think to help you do the calculation I can tell you I can tell you what is this guy so you right in the rescaled variable you can write down that the linear part of the pressure is minus 2 dx u2 so if you use that if you use that you can do the calculations okay so this is good because then what does this mean so if you are in the inviscid case q2 is nothing happened to it it is just conserved if you are in the viscous case you get the enhanced dissipation right so if mu equals 0 q2 is just q2 initial I will say and if mu is larger than 0 we have enhanced dissipation but I'm like in both cases your q2 is bounded let's say it's it's not going to grow or nothing bad is happening to it so then the good thing is that now u2 the way you recover u2 is that you invert this Laplacian l and okay Laplacian l gains you 1 over t square so from here we deduce that your u2 in sobolev norms your u2 in sobolev norms will will be like 1 over t square let's say your q2 initial okay these are this is for the non-zero modes I should say always like non-zero mode referred to the non-zero mode in the in the capital X variable okay so this is type of things you'll be getting this is if you are in the inviscid case if you if you add if you get the viscous effect I mean you can add some sort of exponential minus some constant mu t to the 3 if you add the viscous effect but this is more or less like the type of of course like it's more this decay which is more important than this one in when when we talk about u2 okay so if you remember in the in the 2d case in the 2d case this decay gave us also the decay of u1 for of course for a simple reason that like the incompressibility if you think about incompressibility in 2d I mean like you will write it down as ik if I am non-zero hat plus dy of course like the dy will lose me actually like if I if I write down if you remember the divergence free is like here it is I'm writing it in Fourier so it's like plus i eta minus kt u2 this was equal to zero so in 2d in in 2d if this decays like one over t square this will decay like one over t when k is different from zero okay it's not difficult to see that okay but now we are in 3d and I have to add il u hat 3 so these two guys will not decay okay there's no decay for the other components okay and it's not difficult like to look at I mean you can you can go back to the equation you look at the equation about u1 and u3 and you see that there's no decay mechanism in them I mean of course there is a combination of them there is a combination of them which is good but but there's another one which is not good and okay I mean one can think okay is there like some sort of null good null condition that helps with this particular non decay but no there isn't okay so so the only way you can get u1 and u3 to decay is by enhanced dissipation is really the this type of decay for u1 and u3 and that's one of the reasons why like in 3d we definitely need the viscosity otherwise the result will not be is not correct okay let me go now to the second the more problematic actually effect which is the so-called lift up effect I mean lift up effect this is I mean this is a physical terminology but it has it has it's it's also a simple linear effect that we can understand which concerns the zero mode actually so I mean for the zero mode I mean for the zero mode I mean whether you do this change of variable or not is the same I mean you can see the the calculation at this level or at this level it's exactly the same so you just average in x you take the equation and you average in x and you see what you get so if you average in x you get the following equation so I'm writing it in the new system of coordinate but it's it's not okay so now you remember you remember things from study of matrices I mean if you remember this this has this is like a Jordan block basically right so there is some sort of Jordan block here and I mean this you can solve it explicitly I mean like you have a formula so so think of these as functions of y and z right these are functions of y and z and you can solve it so u01 of t is exponential t mu Laplacian so here it's Laplacian if you think about it it's just in y and z but it doesn't matter u initial 0 1 minus t u20 why I'm not writing initially I should be an initial I'm getting confused what I should put the initial there or not yeah so the u2 and same for the u3 anyway so I mean the way I think about it forget about the viscosity I don't want to think about the viscosity but if you forget about the viscosity which means let's say if you are four times less than mu to the minus one four times less than mu to the minus one you can forget about the viscosity but then you see that u01 will have a linear growth right you'll have a linear growth which we didn't have in the in the in the 2d case so so basically this sort of linear growth means that if you start with if you start with a perturbation of size epsilon and you wait till time so this is at time zero and you look at what happens at time mu minus one then you become of size epsilon over mu okay so this means that you cannot allow perturbations larger than mu right you cannot allow perturbations larger than mu because this simple this simple I mean just looking at the zero mode gives you this and then I mean this is really physically very relevant and it is observed it has has a name it's lift up effect and so if you remember in the 3d case I said in in the Gevry and Sobolev we had like two different kind of size of perturbations here we can allow epsilon actually to be that small constant times mu in the Sobolev we allow it to be of size mu to the three halves so the this sort of size of size mu is basically related to this in the Sobolev it is much more subtle why why the say the size should be this one I mean at least we I mean we don't have the the I said in Sobolev we don't we we don't have the instability type of things but in the in the Gevry we have the instability we can prove that your solution can really do this we can prove that your solution can really do this thing but we can follow this sort of zero mode and we can see it really grow from size epsilon or size mu till size one okay so any questions or before we move to non-linear effects yeah maybe there is another linear effect I want to talk about which which is yeah let let me talk about this even though I mean like it is it is related to the fact that you want it is related to the fact that you want and you three do not decay and we give it a name I mean I'm not hundred percent sure it is I mean at some point we were calling it vorticity stretching I mean it's more like a stretching behavior and it turns out like in the proof it is an important it is an important fact to take into account and even though I think I mean I will not go into the proof but it it shows an interesting thing so I mentioned that q2 was was already introduced by by Kelvin he didn't look at the whole Laplacian he only looked at Laplacian of u2 I mean he thought that Laplacian of u1 and u3 were not interesting and I mean at the beginning we we were trying to do estimates on u and q and q but then after some time you immediately see that since you are taking the Laplacian of u2 you have to take the Laplacian of all the other components so so that's how we introduced like q which was the Laplacian of u and capital q which was the Laplacian l of capital u so this is in the original in the new variables and then I mean you can write down equations on q2 and q1 and one one one nice fact so let me write down just the linear case so then I get some Laplacian l of q2 so this is the time derivative and there are bunch of terms sorry q1 so there are terms that come from the q2 and then there is another term which is something like this dx dx dy dx dy l if you remember the notation this means it is a dx dy l dy l is is this guy okay so there are other terms so you you just try to see how really um yeah so at the linear level this is what you get equal zero so why why I wanted to explain this sorry so this is u1 here so um so in a question like this like we said that q2 is not u2 is decaying so this is a good term q2 nothing is happening to it it's like a constant so this normally can give you some sort of linear growth of this guy but actually it turns out that this guy will grow quadratically it has to grow quadratically because um I mean I can recover I'm always talking about non-zero modes I can recover u1 I can recover u1 by inverting Laplacian l minus one of q2 q1 right and I said that u1 was not decaying so if I'm saying that this does not decay and I know that this gains me one over t square this has to grow quadratically and actually the quadratic growth is coming from this guy and you can see you can see that there is a quadratic growth because then this guy actually write it as Laplacian l minus one of q1 okay and um I mean if you if you forget about the viscous effect you can see I mean it's it's an ODE also an ODE and the factor two here is important it's actually the factor two that gives you the t square um the t square right so basically I mean um what you get you get I mean like to mimic the ODE you get you get something like this um plus or minus I think it's minus two q1 over t you get something let's say if you mimic it a little bit you get something like that and this gives you quadratic growth um one of the reasons I'm also mentioning this is that um so if you remember when I met when I talked about the toy model so we still have like 10 10 minutes Frank or 50 oh okay okay good so at least I can explain I'm going to explain few facts like that are new in this proof without really trying to go into um basically I mean if you remember in in the in in the 2D case I explained that the norm has to be built based on that sort of toy model here we also need to take a norm that is built on linear effects and non-linear effects so in particular um one part of the choice of the norm is based on trying to control this sort of growth by the by the Laplacian right um I mean again this I mean here I'm talking about something which is about the non-zero modes right it's about the non-zero mode and I explained that I don't want this non-zero mode to come and destroy this sort of growth that I'm having here I mean at the end of the day I want really to make sure that this is the main thing that is happening and that all the rest is under control so um so then we write we introduce a multiplier that more or less may make the growth that you can get from this and then there is a time where this kicks in and and this the decay coming from here will overcome the growth so so basically you can see that your Q1 start growing and then decaying but now the decay is coming from the viscosity not from some inviscid effect like um like in the 2d inviscid case okay so that was another linear effect um that I thought was interesting to to to to mention um okay so let me now talk about non-linear effects unfortunately I will I will not tell you where why the Jovray 2 here happens I mean here if you I said in this case we need Jovray class 2 and here we need like some sobolef but the Jovray class 2 here is coming from a toy model like the toy model I explained for 2d oiler but they have nothing to do I mean it's it's much bigger toy model that involves that involves um writing a system of equation on Q1 Q2 Q3 right so I showed you the linear part of Q1 it's already has many terms if now I write to the non-linear term and it has like maybe six terms like you have to now one of the difficulties here is that you have to keep track of Q1 Q2 Q3 separately because each one of them has different properties so I will not really try to give you the toy model that may make the worst growth that will tell you that you have to take that Jovray but instead I want to mention um some other thing about the change of variable actually so I want to more um yeah so I'm going actually to mention two things I want to mention two things one of them is the change of variable and another one is some sort of null conditions in the non-linear terms so these are the two non-linear effect I want to mention so the change of variable so let me put back the non-linear term so I have a change of variable and some sort of null conditions here I don't know whether this is right terminology but we are like borrowing terminology from the dispersive word just just to mention that the non-linear term has built into it some nice cancellations and that um I think for people familiar with Navier's talks like many of the results about Navier's talks can be proved by replacing u grad u by anything that looks like a derivative I mean quadratic term with a derivative it turns out I mean in this result we need a lot of the precise structure of course like here we are losing but we are not losing too much basically and um in this term let me mention this first because I think I I mean I think it's important to keep this in mind so in this term I mean you have growth but it turns out um there are two interesting facts that do not happen in this term and one interesting fact is that the u01 so the u01 is the worst guy I mean the the guy which is growing so there is no um self interaction of the u01 with itself because like you can see here the u01 comes into the first component so the first component comes with u1 dx of u so if I if I look at the first component the first component of this so then I will get u01 u1 let's say but then there is a dx here so if I put u01 and u01 this term will disappear so u01 does not um does not appear quadratically in the nonlinear term so that's a good effect that's that's one one thing that we call um I mean if we had a term like that all these exponents will be much worse okay so so this is what we call like a non-self interaction of the u01 okay so that's one was no self interaction remember that I want things to to look more like the linear thing so I want the non-linear term to be the weaker possible so that was one effect another effect I mentioned here that I have this gradient l and this gradient l is bothers me a little bit because there is a t in it but and a good thing is that this guy I mean if I write down the if I write down the convective term I will get something like this this is the convective term right okay so what what can we observe here this is bad this will lose me a t but the good thing is that this guy the guy that loses you a t is always paired with the guy that decays better right so I said that this guy decays like one over t square so the the bad growth that you have here is always comes always with the good decay of this guy versus like here this guy is not decaying but it comes with a derivative without a t so so at the end it balances well so somehow that that's another good effect from the non-linear term that um that was important also okay so um those are at least the two main things that you can really that I can really like explain in a simple way I mean there are many hidden other small things that you see in in the course of the proof but let me not talk about them okay um okay so let's let's let me now go to the non-linear non-linear change of variable or maybe before that I like to yeah since I will not have time to give theorem but um yeah maybe before yeah maybe I will not give you the change of variable but instead of that um what comes with lift up effect so in the physics literature you will see something called lift up effect but you see another terminology which is so called streak okay so what is a streak so um these are related to what is called 2.5 solution of navier stocks so it has to do so what does that mean these are solutions these are like solution that depends on two dimensions but they have three components in them um and the so the two the two dimensions here are actually y and z okay so so here I just explain the linear picture but the non-linear picture for the zero mode so if I if I look at the zero mode so if I call let's say v equal u0 of yz you can see that um so now I'm back to the non-linear equation for if I take that it's it doesn't matter what I do I work in the original variable or in this then you can see that actually v v2 3 actually solves two d navier stocks in yz and this is well known in the physical literature people are and then the the u0 1 or in my notation will be like v1 v1 the v1 here I just wrote the linear piece will be solving some sort of drift diffusion so it will be solving an equation that will have a v2 3 in it also v2 3 grad yc of v1 equal minus v2 okay it's a scalar minus v2 plus mu laplacian yz of v1 okay so that's really the the equation that you get and this sort of v will be called a streak because it is like a two dimension solution of navier stocks in yz now right so you have to change like the way you think about things and then you have some sort of linear growth right so so basically this is exactly this same picture but at the non-linear level so somehow it's really saying that the lift up effect which is like a sort of linear thing survives in a nice way in the non-linear case okay okay now the picture that we have now so I think I mentioned in the jeuvre case we have two results with Pierre Germain and Jacob one of them is to prove stability if I start with epsilon smaller than this and the other one is to prove sort of instability if I start exactly of this size so in the in the instability case I would like to show you I mean it's more like applied math type of way is to show you what's going on really what's happening why why we have these results so basically like if you start at t0 you can start with the data which is of size let's say epsilon epsilon less than some constant times mu at time zero so now if we put all these effects that I mentioned lift up effect enhance dissipation inviscid dumping if you put all these effects together what's what will be what will happen first of all if you go till if you start with if you go till four times larger than mu to the minus one third so the first times are these times so this is the time where enhance dissipation acts so what will be the effect of enhance dissipation it will kill all x dependence okay so no x dependence so so then what happens that your solution your solution will approach streak so that's in the physical literature you will see that as like what they call like metastable effect metastable state so you approach something which is not your the state to which you are converging but you'll be close to so we become close to a streak okay so that's the first thing that happens okay so then when you get till times like one of a new when you get till times like one of a new there are two things that's happening first of all the u01 u01 will reach more or less its maximum it will be like epsilon over new and then okay depending on depending on how I choose this constants so if I choose this constant really small very small so it can become it starts so then my your my u01 start like epsilon can become of size let's say one over million but then decays so you can follow all this in the good case so then that's where like for instance we get these two possible results either either we stop like either we say okay at this time if that c0 is large I get here till something of size one and then my proof stops I cannot control afterwards or if if I start with epsilon if I start with epsilon let's say which is smaller than very small constant times new for times larger than one over new so for times much larger than one over new then the viscous effect in the regular viscous effect will kill also the yz dependence and then that's how you go back to your quit I should say that this picture is correct in the jeuvre case in the sobolev case I don't think it is correct that there are many other non-linear effects that can start becoming important but we cannot really say precisely which ones maybe it's a good time to stop I guess so if c0 is big you say it goes out of the window but you don't know exactly what happened okay so actually I wanted to say that so so basically what we expect and I think if I'm not wrong this is what people doing I mean like in the physical literature trying to say so so this is a function of yz right so this is a function of yz so what happens is that you start seeing oscillations in z and now oscillations in z normally gives you growing modes right so for those who are familiar with shear flows if you take sine of y as a shear flow I mean there are cases where you can have growing modes so so what what is really expected is that this if this starts becoming of some critical size it will give you some instabilities in in in z direction so that's that is what is expected I'm hoping to see how I can prove results like that but it's really tough like I think a good result will be to start with the data start with the data like I mentioned here put the right amount of energy in a bad mode for this guy and hope that after you wait the right amount of time that guy that mode starts growing it's it's not clear whether one can prove such kind of things but but I think I think if I'm not wrong like some some experiments will see really like some sort of growth then you get some sort of turbulent behavior and then it becomes laminar again so somehow what you what is possible is that you reach a time let's say at this time some growth can come from z directions so then the Laplacian start killing things better and then you go back I mean I have to go back to some applied math talks where I saw this kind of things but trying to maybe now I understand the much better anyway yes no no more questions


Hello, my name is Alan Williams and I'm reporting from New Haven, Connecticut And I'm here to provide the next installment for the Shia news update This installment will be for the week of August 14th 2015 This was yet another deadly week for Shia Muslims as over 60 were killed and over a hundred and forty were injured most of these deaths occurred in Iraq and Since the deadly Jamila bombing last week There have been multiple bombings throughout Shia neighborhoods both in Baghdad and in other Shia neighborhoods Around the country these attacks mostly perpetrated by ISIS have taken over 20 lives and Have entered over a hundred In a separate incident ISIS has video pictures have emerged of ISIS executing at least five Shia Muslims in the town of Kirkuk Details are continuously Emerging but as they are made available They shall be posted on the Shia rights watch net website and on our social media in Bahrain yet another Shia cleric was arrested Sheikh Hassan Issa was arrested in the Bahrain International Airport shortly after arriving with his family Details have yet to emerge on The reason for his arrest or any charges that have been filed as this information is made available again They they will be on our website and on our social media platforms For this and other information on Shia news around the world Follow us follow Shia rights watch on Facebook Twitter Instagram or LinkedIn or go to www.shiariteswatch.org


I get questions from women all the time about men who want far less than what they want and they want to know what they should do about it. So look, I don't know you, I've never met you, but if you're listening to this, my guess is that it's a message that you need to hear. You are worth more than that. He wants to hook up, hang out, and get the benefits of being in a relationship with you without calling it a relationship. He wants to see other people because monogamy isn't realistic, but you're expected to only be with him. He wants all the benefits of being in a relationship, but when you talk to him about being in one, he's confused and unsure or not ready. You are worth more than that. He wants to disappear for weeks at a time with no message and pop back up in your life like nothing ever happened, expecting you to let him back in. He wants to pretend like you're in a relationship together, but when you're out in public or around his friends and family, you're just a friend, his dirty little secret. You are worth more than that. If you're used to being treated badly, taken for granted, pushed aside for something or someone else, you may start to believe that you don't deserve what you want. You get what you tolerate. Remember that. If you want something more, stop tolerating less. If you don't, you'll end up settling, looking back on your life and wondering why you were cursed. You have to believe that you're worth more. Believe that you're valuable. Believe that you deserve more because in reality, you won't be cursed, you'll just be cursing yourself. He wants a relationship with you. He wants a relationship with someone, but not with you. With you, he just wants to be friends with benefits.  He wants no responsibility for how he acts or his part in the relationship. You deserve more than that. He avoids discussing topics that are important to you. He wants to get all of his needs met, but he doesn't care if yours are met or not. He always tries to push past your boundaries instead of respecting them. You are worth more than that. Now you may be asking yourself, but Matt, what if I stopped tolerating it and he leaves me? The real question that you should be asking yourself is what if you keep tolerating it and he stays? He keeps treating you the same way.  We have women in our community that have experienced this.  His one and only, the love of his life. He disappears and hides when you need him instead of being there for you. You're totally in love with him, but he only feels mildly interested in you. He's abusive to you mentally, physically or emotionally. You are worth more than that. He's waiting for you to pursue him, contact him, invest in him while he doesn't do any of those things in return. He ignores your calls, texts or messages for days or weeks at a time. A guy sends you one, a one word message. You are worth more than that. He texts you forever, never setting up a date, never calling, never moving things forward. He wants to casually date you for 10 plus years without moving things to something more. He hides from you.   You are worth more than that.   So the next time a guy acts mediocre around you, just remember you are worth more than that. The only reason men do this is because you let them get away with it. It's time that we set a new standard. If someone else wants to put up with this fine, but you're worth more than that, your beliefs determine what you experience in your life. If you believe that you deserve to be treated poorly, you'll accept people in circumstances that are beneath you. If you believe that you deserve something more, you'll pass up on those people in circumstances because you know that those are not for you. You can't believe in scarcity and have abundance. You can't believe that you deserve to be poor and keep wealth. You can't believe that you deserve to be treated poorly and keep a man who treats you well.  You need to raise your standards if you want something more. You need to say I deserve the best. I am blessed. I am beautiful. I am powerful. My suggestion is that today, right now, you shift your mindset. You believe that you are worth more than that and only allow in what's worthy of you. Watch how things change and turn around in your life.


Since its inception, the Hart Institute has been synonymous with several pillars. Clinical excellence, innovation, and, importantly, education. The General Cardiology Fellowship here is extremely competitive, and the Fellows are absolutely top-notch. We expect our Heart Failure Fellows to mentor the General Cardiology Fellows when they rotate on our service. There's a very special ethos and a very special culture about the Texas Heart Institute. It's really a deep bond that we have between each other, and you can't get that unless you spend time here. Beyond the clinical rigor, you have a remarkable way to think critically about problems. You're technically excellent, and you're committed to excellence in lifelong learning. And I think those concepts are so important. Our program currently has the best survival of any transplant program in the state at 97.5%, and some of the best in the country. We're more excited about our future than we have been in the past, and so we're eager to move this ball forward.


You need the right ingredients, the right tools, and a little bit of finesse to create the masterpiece. In this case though, the ingredients are honesty, patience, and empathy. You can't expect to whip up a gourmet meal using expired milk and stale bread, so don't skip on the good stuff when it comes to communication. And just like a chef needs the right tools, you need to choose the right words, the right tone of voice, and the right body language to get your message across. You need to know when to turn up the heat and when to let things simmer. So channel your inner Gordon Ramsay and spice up your communication with honesty, patience, and empathy.


My first small step was finishing my undergraduate degree here at Purdue, which involved two semesters of undergraduate research. That led me into my second small step, which was deciding to stay at Purdue for graduate school in chemical engineering. And as part of that, I did a 10-month internship externally with ExxonMobil, which allowed me to get that industry experience, that first opportunity to get my feet wet. Coming back to Purdue, to finish that degree, the third small step I took was landing that first industry job. My giant leap was becoming vice president as BP Pivots from a hydrocarbon oil business into an integrated energy company. Kyle Kastraski, PhD, chemical engineering, 2008. I am a Purdue engineer.


The guide-on records the contributions of past service and ensures inspiration for future sacrifice. The guide-on bearer. The enlisted soldier who exemplifies the highest standards of history, conduct, and military expertise that may responsibility in burying the guide-on. It represents so much who is our soldier. It's been a great opportunity for me. And really truly my final vote that I want to make, because I'm pretty important to me here at Fifth Board, it's a really sentiment that I want to leave with the men and women here. A lot of you may not like exercises, force packages, and staff work. That comes along with being in the core headquarters. On the ones that I still keep in contact with, or with any other unit that I've ever been in. It was probably one of the things we got a great job bringing in here that I think we're going to have a really strong command team to really continue what CAC parts are worth. At Soldier's Time in Fifth Corps, if they spend three years in Fifth Corps, they're going to spend at least one of those years overseas. Every day for a forward mindset, you probably won't find it, but you're going to find it here. So with that, Sean...


How's it going everyone Caleb here with the late in sports cards next night. We have 2021 prison basketball Six bucks have case break number 17 pick your team style Lay right off the teams that you guys do have Aaron C Celtics Daniel L Clippers Eden R Kings Edgar B 76ers Eric W Thunder Harper B Mavs Grizzlies jazz and Wizards Jeffery H Nets Nuggets Jing H with the bucks June W K spurs Kyle T Warriors and T Wolves Mike H Nix Miles H Blazers Got Noah B magic Norris L with the pistons Patrick Z pelicans Patrick F Suns Raquel B calves Sacco K with the Raptors Sean M Lakers heat Steve S with the Bulls Ting Y with the Pacers Tray H Hawks Wong as Hornets and Yip H with the Rockets. Here we go. Best of luck after this Do you have a hobby and photo two box mixer and then a full case tiered random teams? Close out the evening for your group breaks Sam will be going for a little bit longer with the personals then after that there is still a little bit of space correct Grab something if you want something it's getting close though to Exactly Would order it very soon if you want something it's getting close Kendrick Nunn silver Marcus Morris there Zach Levine Chris Weber Jalen Green on the base rookie great start You go nice green Rockets right off the rip there. Yep Great car to start Get red wave Cal Lowry Montrez Harrell on the hyper fireworks Paul George Eva Johnson base Silver Wendell Carter, it's gonna be a blue David Johnson cracked ice to 125. You go Raptors Solid 75 years silver Larry Bird IU Paul Sar Jason Tatum nice card last spot mojo there to 99 Malik Beasley Luca nice one on the Tatum there congrats Silver Noel hyper shake Milton I Say a livers and Delano. I can't they always put these drop rookies at the back. It'll be nice Hyper MP'd Josh giddy this time base rookie autograph.  They're just a little more frustrating deal with in the packs here Silver Kendrick none Basically Rob to 299 camp Thomas Basically coming up base That's another way to put it and you wouldn't necessarily be too wrong And it's gonna be a red wave miles bridges Get a purple cracked ice Marcus more senior to 149 Open same goon Jalen Johnson rookie Went to Taco Bell the other day. Yeah, I think they doubled my order on accident And paid just the price of whatever the heck I actually ordered First time it's like wow silver Jared baller chads hyper draws in Lillard Trey Murphy It's like, okay Yeah It's an always go in your favor, but nice when it does Usually you're like missing two things We got a Malachi Flynn their blue cracked ice to 125 Yolk it's Santiago Mata or option C Rob would be worth a lot Because if it is good conditions, and it's none of the things I mean warped doesn't matter for green It's sending the most warped card ever Killian Hayes to 299 red but still just Making a joke back Name is key to silver Anthony Simon's 75th anniversary rookie Brandon Boston jr. Clippers Seven of 75 nice. There's no way. This is gonna be a real play. This isn't gonna end in your favor Rob is not gonna say a real player here Rick, excuse me.  What do you got for me Rob? Although I'm Very cautious here Evan Mobley on the base There he is nice base Mobley. Is that short print or something? What are you talking about? Gregory Trey man Brandon Boston jr. Red wave Steve Nash Hi, Bertie Andre Jordan Sam is thoroughly confused her Man he is thoroughly confused. It's a magic card These are spring to a magic card Cory kids You got Sam Rob. You really got me. I'm she walls black gold Dwayne way Awesome hit there Miami heat Jersey number That's sick.  Gregory is numbered to 75. That's awesome, man There you go heat three of five Grab me the brain of Boston That's There you go hang that of course by your works the honest So one more time This is the brand in Boston jr. Right here 75th anniversary parallel in the front It is numbered to 75. Yeah, that's that's big. Yep Rhymes Bones Highlands Paul Sar James Wiseman second year You're all good. Gregory. You're all good. So there is also a 75th anniversary Parallel that is like an insert more so it has a 75 in the background and that is what I was referring to If that makes sense It's the brawn there for your list Kevin Durant So you were listening correctly. Just there are two different 75th anniversary things So that there is the red cracked ice parallel and then there is also like an SSP 75th anniversary insert that is not numbered. It just has a big 75 behind a Star player Chris Duarte base Silver Harrison Barnes.  So hopefully that helps you out a little bit Ridiculously short printed. Yeah If I had the picture still on standby or the card, I would show you it's already out though shipped out Oh Bam on the purple there you go heat again to 99 for the next year autograph Jerry Lucas You go Nick's Nice up from Saint Goon Jalen Johnson rookie silver Kevin Durant's Tray young prismatic We got Trey Murphy Dennis Schroeder red wave hyper Cole Anthony Santiago Mata silver Darius Garland. We got an orange Bismarck beyond about a 49 I see a Jackson Yannis. I really hope so those are so tough to hit. I'd love to see one this break It would be a big big hit red wave RJ Blue Bogdan Bogdanovic to 199 Curry fearless So confused by this parallel because I was the optic on the bottom Mm-hmm. I know I put this into the wrong Silver Charles Bassie Anthony Hardaway hyper. No, I know it's strange. I don't it doesn't make any sense. Yeah, no idea why it's just like the What's it called the Yeah, not supposed to be like that Look next box box three Duarte base Christopher base silver Kyrie fireworks silver Devin Booker LeBron River Jones Toscano Anderson red wave Tyrese maxi hyper Collins Sexton Fear this Luca Yeah, I don't really know if there's a whole lot of them on eBay that you can find right now Yeah, if that's where you're trying to find one Gregory Honestly, there might not be a lot on there John Morant on the orange wave to 60 Silver 75 years. I have no idea how many of them they made But not a lot So I would expect them to hold a pretty good premium for a long time on the base Jaylin Sugg space Red wave three rose here blue Jay Sean Tate to 199. I can't stack anything with these warped cards, man It's just like two stacks and it's right over to you Bobby Ford is there on the hyper Jared Allen silver I'm gonna look out Just tiny stacks of these You can't do anything with them over here though. They just collapse McBride. There we go red Evan Mobley boom Big card 205 of 299 That's nice Beautifully centered copy there on the mobley. We'll mag that that is beautiful. It's beautiful. There you go cabs Silver Marcus smart ray young silver mindset Raptors Vince Carter autograph base nice That's cool. Take a little Vince Why not All right, one-to-one times. I are Williams Wise camp Luca red wave hyper Roshan Holmes. I see you have prism coming up in your queue tonight. I do interesting Just be careful the shimmers sometimes are backwards, so don't get thinking it's an auto Exactly that's what I mean. Just be careful on that Franz Andro silver clay Thompson, I wish I didn't say anything. That's you 46 up 99 color match Davion Mitchell boom That's sick That is sick for the Kings We'll mag that there you go Kings That's a really nice Kings parallel there That'll be one of the best Davion parallels to have Cade Cunningham on the base for sure Pulsar Joe Val Nicholas Batum blue cracked ice to 125 Yeah, that's really nice That car will be slept on a little bit here in the break Davion Mitchell silver for me a Hyper Isaiah livers Should the Kings are thrilled to see something like that as well in addition. Oh, yes, I love you all of these beautiful beautiful What's it called? Cards that just want to be extra warped Isaiah Jackson Reggie Bullock on the purple cracked ice to 149 and a silver box auto bobby porters. There's a one per case when I'm rippin Those a box second half guys a two box or next and then a full case tree Cooper silver MPJ silver mindset curry redemption Yep is Kevin Durant Flashback signatures prism silver Boom, that's nice I'm going to yeah, I'm gonna double check right now I'm gonna double check. I'm gonna double check. I'm almost positive.  That is not supersonics. No That's Nets No, yeah, that is Nets wanting in with the computer Yeah, all good. I was checking to check this flashbacks signatures sets Autograph is Nets guys. Yeah, I'm Thomas Bill Russell Red waves your my Robinson Earl Thunder there. It's gonna be a Ray Allen hyper Give it a rant fearless Great hit Nets. I'll be sick Scotty Barnes base Silver Xavier Tomey and blue Taylor Horton Tucker to 199. I'll be really nice when it does come in Kaminga base Jared Butler base Tony kooko. It's on the pulsar bulls red wave Kelly olinic to 299 Silver Lonzo hyper Brandon Clark They live hers Jeremiah Robinson Earl It's gonna be quite Leonard hyper Chrismatic BJ Armstrong number to 25 mojo autograph for the bulls to 25 you go bulls Nice Is it Todd Paul George Silver Fireworks Silver Zion sky Vaughn Stanks. What's that? He's making fun of Red Sox I ain't got no issues. Caleb also staying so I See no problems. Davion Mitchell Red wave Malik monk. It's gonna be a city osman hyper fireworks Katie It happens I say Jackson Silver Facundo Compaso and an orange Herbert Jones That's nice 29 to 49 Congrats there Helicans There you go. Well, it's awful that went up very nice Herbert Jones Last book it's a nice hit Sam a Red Sox Yeah, yeah red socks all the way Red Red Nicholas Klaxon to 299 Yanis He actually has a hat on right now. Yeah, I definitely do not Primo book night Silver Lori marketing hyper RJ Call George he loves Red Sox cards as well Unless they're making the money I don't Said he has a special box with all this red socks Yes, I do Moses moody You guys heard it here first Daniel dice there that's purple cracked ice to 149 Yanis Yanis That is most definitely not true most definitely not true Red Sox Steelers all the way I can't think of like two Franchises maybe the New York Knicks would be the only other franchise I'd want to like root less for oh man between those two maybe the bangles Maybe the mat one of those those franchises one on time. Here we go. Here we go You won't pull one one true you won't you're scared I Santel mod up the red there Kendrick none to 299 a little brawn Keon Johnson Jaden Springer silver Jason Tatum silver Damian Lillard There he is Bobby Portis box auto one per case when I'm ripping You go box only when I'm ripping I don't see anything else in them like this Charles Bassie red wave Charles Bassie and a hyper Chris Duarte Pacers nice hyper rookie Also, if you do want to be upset with someone today Cortes did gather the cases Also, if you do want to be happy with someone today Cortes did gather the cases So it's up simple 10 you're in Wiggins silver Gorondrogic and a blue Gorondrogic to 199 Yeah, Steve is here. Don't worry We're keeping him safe keeping him safe coach Dwayne Wade Pulsar why not? You are on the way to the rainbow There you go. He Orange Tyrese Halliburton to 60 not bad that Wallace Sleeven with the best of them over here simple 10 this guy Modering right on through this prism. Oh, yeah That is a Evan Mobley base. There you go silver Mason Plumlee hyper Donovan Mitchell There's a Yanis basin there and they grab that you'd be sleeving and he'd be top-loading. Oh, yeah Jeremiah Robinson roll hyper Damian Lillard fireworks I'll just sumo bowls base rookie auto there bowls. There you go nice Jalen Green on the base rookie. There you go Solid Arbor Covington silver Lonzo Silver fireworks and bead best card tonight. It would be a Scotty Barnes mojo. Let me the best hit of the night Number to 25 on those red wave print forms hyper Monty Morris Anything else you got for the number two spots in There's number two would maybe be like the Jalen Green blue Definitive might have beat it Yeah, probably that yeah, that's a no Compaso blue to 199 Allen Iverson silver The Scotty is huge. Oh, and that is firmly in the one spot Firmly in the one spot Keldon Johnson on the red wave there Miles Bridges purple cracked ice jaw. Yeah, the Scotty is just Just a dream hit Aaron Wiggins on the silver rookie hyper Bismac and want to go guys Luca auto redemption we also the Katie auto redemption. Yep. Yeah, we're doing good on the redemptions last box guys So there's a couple hits for you all of which have been from prison basketball We have done a load of prison basketball tonight though. So it does make sense Corey Kisbert That's a Pulsar Aaron Gordon purple cracked ice that young 149 and Grimes silver Joe Val hyper Isaac Acoro Levine Jamal Murray bones there Chris Duarte Zach Levine hyper prismatic And Pacers again Chris Duarte base auto you go Pacers solid Nice one there teachers congrats very nice Scotty Lewis Aaron Wiggins Silver Larry Nance Jr. Silver prismatic Luca and autograph here for the Clippers Jason Preston base auto Clippers red wave Kenyon Martin Jr James Harden on the hyper Bradley Biel There's Keita Evan Mobley on the base Silver Delano Fireworks I on little to go guys little to go here. Good luck on the rest of it Santiago Mata red wave Chris Middleton not numbered red. I say it's hot to 299 Anthony Davis Man, oh man, Rob your life once again. Your life is just the best Rob. There's always something going on Silver Aaron Naysmith not always good, but always something bio de sumo on the hyper rookie. There you go bulls That's just great Rob.  Yeah, blame the cats. I agree Charles Bassie 75th anniversary for the heat Jimmy Butler What a break there Heat congratulations True Rob, you should go check on them right now. See what's popping off there. I Oh, just soon Jason Preston silver Terrence Ross silver mindset, Hawaii fearless Barclay Red wave Deandre Hunter hyper kuzma exactly wrong Trey Murphy silver on the Herbert Jones. There he is Blue Tracy McGrady. That's clean 2199 magic 75 years dating Thanks again guys. Let's do a recap here. I do appreciate you joining that one very solid stuff Recap recap coming up. All right autos here notable color in the mags Jason Preston Chris Duarte. I hope to sue me Bobby Portis orange Herbert Jones to 49 That is gonna be a mojo autograph PJ Armstrong 25 silver Bobby Portis Vince Carter Jerry Lucas Brandon Boston jr. To 75 Kobe white Tom googly autumn David Johnson there. It's blue cracked ice to 125 purple Davion Mitchell Josh Giddy's sensational signatures red Evan Mobley The redemption Kevin Durant for the Nets flashback signatures prism silver and The black gold d-way 3 of 5 Thank you again. I appreciate it guys. We'll have them all protected and sent right out to you Good luck in the next one tonight


Sally Dale lived at St. Joseph's from age 2 to 23, perhaps longer than any other child. She said the nuns there beat her regularly. That photograph is a photograph of you at a time when you were receiving virtually daily beatings at the hands of people at the St. Joseph's orphanage. Yes, sir. Repeatedly locked her inside a small container that was kept in the attic. I could not really sit up straight. I definitely couldn't stand up and you really couldn't lay down flat. And sexually abused her. After whatever happened in her bedroom, she'd bring me by the hair and bring me back to my bed.  In the morning when we got up, she would have me sitting on the floor beside my bed and she would make all the other kids laugh at me and tell them what a bad girl I was during the night. But those aren't the most serious allegations. I saw somebody push a boy out the window and I was looking up at the building and to tell you who the nun was, I can't say, but I knew it was a nun because she had to have it. And he kind of hit and... Bounced? Well, I guess she'd call it, it was a bounce. And then he laid still. Sally also said she saw a boy drown after he was thrown off a rowboat and into a lake. All I said is, did he drown? Who'd you say that to? To the nun. And she said, oh, don't worry, he's gone home for good. This is Ed Dupri explaining how he was thrown off a boat. I was fighting for my life when I was swimming ashore. Did this happen to other children? Oh, yes. Yes. All the time that I was there, it happened. Every summer. Patty Zeno said a nun named Sister Priscilla tried to push her off a windowsill when she was standing on the outside washing the window. The windows were open, probably like this, so that they could hold you by your ankles. And she just went... And what happened? I started to fall. We don't talk about it at home. We don't... It's not conversation we have over tea. It's... We just don't. And so now maybe with this, we can start telling more of those stories because they didn't even know about my own shirt story. Wade Khochwade up in Elia, in Canada. Phyllis Webstad, Rens Klagst. Strachem Khatlem Stakwen. Hello, everyone here in Canada. My name is Phyllis Webstad. I'm from the Kennew Creek Dog Creek First Nation in Sawep Mchuluch, the land of the Shuswap people here in Williams Lake, BC. I am third-generation residential school survivor. My grandmother attended for 10 years, along with her 10 children. When I turned six in July of 1973, Granny brought me to town to buy something for my first day of school. I chose a shiny, new, orange shirt. It was bright and exciting, just like I felt to be going to school for the first time. When I got there, my shirt was taken away, and I never wore it again.  You will make sure that this history is never repeated. When I see people wearing an orange shirt or an Every Child Matters pin, for us survivors, it's like a little bit of justice in our lifetime for what happened to us. Cookstjamr, thank you. The Williams Lake First Nation revealed the results of its preliminary investigation at the site in just one part of the grounds, separate from the cemetery. They found 93 potential burial sites, and a warning, the details are disturbing and could be upsetting. The earlier pin to see, my sound and weight could be as was tells in the earlier version of your yard to be so ach. My sound and weight could be as per constant weight, or weight could be due to some genes, or it could be canoondles, and earlier, the height, to be so ach. Doc's children were sleeping for quite an estimate quite a slight amount quite a good judge and a weight could be as was told in the earlier version of your yard to be so ach. The earlier pin to see, my sound and weight could be as was told in the earlier version of your yard to be so ach. Doc's children were sleeping smelt, weight smelt, due to some genes, and weight could be as was told in the earlier version of your yard to be so ach. Doc's children were sleeping as was told in the earlier version of your yard to be so ach. Doc's children were sleeping well, well, well, well, well, well, well, In the beginning of the 19th century, there was a group of young people, young people from different regions of the country, who lived in the countryside. In the beginning of the 19th century, there was a group of young people, who lived in the countryside. Next year they came and lived and distanced themselves in the countryside. The citizens started working in the countryside as well as those living with elderly and old children.  It was really traumatizing. 93 is our number. I wanted to just state, although WLFN has been leading the technical exercise and investigation at St. Joseph's Mission, there was multiple nations that were impacted by the legacy of that school. Chilcoteen Nation, Degeth Nation, New Hall Nation, other Seguepin communities in the Seguepin Nation, Statlium Nation, to name a few. We, and the Degeth Nation, have been living here for years. We have had it for seven years. We have been here to help these children. We are doing our best to help the children. We, as a community, have supported them, and we have been doing our best to help them. I will say prayer for the children who cry and no one hears, for the children who wake up hungry and go to bed hungry, for the children who are missing and for those who are lost, for the children who suffer alone because they have no one who cares, for the children that no one loves. I will pray for these children. You read books, that's cool. All I really want is an honest apology and for them to come face to face with me, tell me these things did happen, honestly tell me that they were sorry it happened and that would they please, if at all possible, never let it happen to children again. Reconciliation cannot happen without the truth. It begins with the truth, the foundation of truth. No matter how sad or how bad their truth may be, it must be told. The future belongs to the children, all the children, all the children. Our children matter, you matter.