Regularity criterion in terms of BMO-type norm of the pressure gradient for the Navier-Stokes equations on unbounded domains

Abstract

In this note we consider the initial-boundary value problem for the incompressible Navier-Stokes equations on unbounded domains in Rd by imposing the non-slip boundary condition. Then for locally uniform domains, introduced by Jones [20], we present a sufficient condition in terms of the BMO-type norm of the gradient of the pressure for the regularity of Leray-Hopf weak solutions.