Interior regularity criteria for suitable weak solutions of the Navier-Stokes equations

Abstract

We present new interior regularity criteria for suitable weak solutions of the 3-D Navier-Stokes equations: a suitable weak solution is regular near an interior point $z$ if either the scaled $L_{x,t}^{p,q}$-norm of the velocity with $3/p+2/q\le 2$, $1\le q\le \infty$, or the $L_{x,t}^{p,q}$-norm of the vorticity with $3/p+2/q\le 3$, $1\le q<\infty$, or the $L_{x,t}^{p,q}$-norm of the gradient of the vorticity with $3/p+2/q\le 4$, $1\le q$, $1\le p$, is sufficiently small near $z$.