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

Alexey P Cheskidov

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.