Regularity criteria for suitable weak solutions of the Navier-Stokes equations near the boundary

Abstract

We present some new regularity criteria for ``suitable weak solutions'' of the Navier-Stokes equations near the boundary in dimension three. We prove that suitable weak solutions are Hölder continuous up to the boundary provided that the scaled mixed norm $L_{x,t}^{p,q}$ with $3/p+2/q\le 2,2<q\le \infty$, $(p,q)\ne (3/2,\infty )$, is small near the boundary. Our methods yield new results in the interior case as well. Partial regularity of weak solutions is also analyzed under some conditions of the Prodi-Serrin type.