On the 3D Navier–Stokes equations with regularity in pressure

Abstract

In this paper, we investigate the global regularity of Leray–Hopf weak solutions to the 3D Navier–Stokes equations in terms of pressure. In particular, we establish three Serrin-type regularity criteria in framework of the anisotropic Lebesgue spaces. Our result can be understood as a generalization of the notable works of Y. Zhou (2006) [23], C. Cao and E. Titi (2008) [5], and Y. Zhou and M. Pokorný (2010) [24].