text: Caffarelli et al. showed that a singularity predicted by these equations would not exist for any finite duration of time.
full_question: Caffarelli et al. showed that a singularity predicted by these equations would not exist for any finite duration of time. They are the subject of a widely cited 1968 paper by Alexandre Chorin. By starting with these equations in three dimensional cylindrical coordinates, one can apply Newton’s first law to derive the Hagen-Poiseuille equation. The “existence and smoothness” problem of completely solving these equations is one of the Millenium Prize problems. Unlike the Euler equations, non-inviscid flow is described by, for 10 points, what equations that describe viscous fluid motion?
first_sentence: Caffarelli et al. showed that a singularity predicted by these equations would not exist for any finite duration of time.