Weak solutions of the Navier-Stokes equations may be smooth for a.e. time

Abstract: Recently, Buckmaster and Vicol proved non-uniqueness of weak solutions to the Navier-Stokes equations which have bounded kinetic energy and integrable vorticity. We review the current developments of the topic, based on the so called convex integration construction, and discuss in particular the existence of such solutions, which in addition are regular outside a set of times of dimension less than 1.

analysis of PDEs

Audience: researchers in the topic

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PDE seminar via Zoom