Regularity criterion for weak solutions to the Navier–Stokes equations in terms of the pressure in the class [formula omitted

Abstract

The goal of this paper is to establish a Serrin-type regularity criterion in terms of pressure for Leray weak solutions to the Navier–Stokes equations in R 3 . It is proved that if the pressure belongs to L 2 ( 0 , T ; B . ∞ , ∞ − 1 ( R 3 ) ) , then the weak solution is actually regular. This improves a result established in a recent work by the second author Gala (2011) [19].