A remark on the regularity of weak solutions to the Navier–Stokes equations in terms of the pressure in Lorentz spaces

Abstract

For the incompressible Navier–Stokes equations in R3, a regularity criterion for weak solutions is proved under the assumption that the pressure belongs to the scaling invariant Lorentz space with small norm, while corresponding results for the velocity field were proved by Sohr. The main theorem continues and extends a previous result given by the author.