Take the 2-minute tour ×  I have to study this system which name
is Navier-Stokes. Can you explain please what means that $p$,
$u$ and $(u \cdot \nabla)u$. What represents in reality? Tell me
please, how should I read the factor: $(u \cdot \nabla)u$? "$u$
multiplied with gradient applied to $u$ " ?  $
(N-S)\begin{cases} -\mu \Delta u +(u \cdot \nabla)u+\nabla{p}=f
&\mbox{in } \Omega, \\ \mbox{div }u=0 & \mbox{in } \Omega,\\
u_{\mid{\Gamma}}=0. \end{cases} $  one more question, what
happens with with the system if $(u \cdot \nabla )u=0$ ? I found
that the system describe the motion of a incompressible viscous
fluid and it suppose the the motion is stationary but no slow,
what means that stationary and that slow?  share|improve this
question This is all explained in the Wikipedia article about
the Navier-Stokes equations. Can you indicate what it is, that
is not clear about this? –  Bernhard Apr 7 '13 at 21:02 if $(u
\cdot \nabla)u=0$ then the system won't be slow ? –  Iuli Apr 7
'13 at 21:04 Can you restrict t