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

Alexey Cheskidov; Roman Shvydkoy

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

Analysis of PDEs 2007-09-06 v2

Authors: Alexey Cheskidov , Roman Shvydkoy

Abstract

We show that if a Leray-Hopf solution $u$ to the 3D Navier-Stokes equation belongs to $C((0,T]; B^{-1}_{\infty,\infty})$ or its jumps in the $B^{-1}_{\infty,\infty}$ -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.

Keywords

navier-stokes equations weak solutions regularity leray-hopf solution besov space ladyzhenskaya-prodi-serrin criterion

Cite

@article{arxiv.0708.3067,
  title  = {On the regularity of weak solutions of the 3D Navier-Stokes equations in $B^{-1}_{\infty,\infty}$},
  author = {Alexey Cheskidov and Roman Shvydkoy},
  journal= {arXiv preprint arXiv:0708.3067},
  year   = {2007}
}

Comments

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

Related papers

View all related →