3D Navier-Stokes equations: the dynamics of a blow-up

I will present an elementary introduction to the regularity/uniqueness issues for the Navier-Stokes equations. Thanks to the convex integration technique, the h-principle is starting to take shape for the uniqueness problem. It might be possible that classical scaling invariant uniqueness results (Prodi-Serrin type conditions) are the only constraints for constructing non-unique solutions of the NSE. As for the regularity problem, the situation is more delicate since there are also dynamical constraints that can potentially prevent solutions from blowing up.



University of Illinois, Chicago; Member, School of Mathematics