Profile decompositions and applications to Navier-Stokes

Abstract

In this expository note, we collect some recent results concerning the applications of methods from dispersive and hyperbolic equations to the study of regularity criteria for the Navier-Stokes equations. In particular, these methods have recently been used to give an alternative approach to the L 3,∞ NavierStokes regularity criterion of Escauriaza, Seregin and Šverák. The key tools are profile decompositions for bounded sequences of functions in critical spaces.