On the regularity of weak solutions of the 3D Navier-Stokes equations in $B^{-1}_{\infty,\infty}$

Alexey Cheskidov; Roman Shvydkoy

paper

On the regularity of weak solutions of the 3D Navier-Stokes equations in $B_{\infty, \infty}^{- 1}$

arXiv:0708.3067

Abstract

We show that if a Leray-Hopf solution $u$ to the 3D Navier-Stokes equation belongs to $C ((0, T]; B_{\infty, \infty}^{- 1})$ or its jumps in the $B_{\infty, \infty}^{- 1}$ -norm do not exceed a constant multiple of viscosity, then $u$ is regular on $(0, T]$ . Our method uses frequency local estimates on the nonlinear term, and yields an extension of the classical Ladyzhenskaya-Prodi-Serrin criterion.

updated version -- a reference was added and a bug fixed

On the regularity of weak solutions of the 3D Navier-Stokes equations in B∞,∞−1​

Abstract

Cited by in corpus (2)

On the regularity of weak solutions of the 3D Navier-Stokes equations in $B_{\infty, \infty}^{- 1}$