A generalization of some regularity criteria to the Navier-Stokes equations involving one velocity component

Abstract

We present generalizations of results concerning conditional global regularity of weak Leray-Hopf solutions to incompressible Navier-Stokes equations presented by Zhou and Pokorný. We are able to replace the condition on one velocity component (or its gradient) by a corresponding condition imposed on a projection of the velocity (or its gradient) onto a more general vector field.

Comparing to our other recent results, the conditions imposed on the projection are more restrictive here.

Keywords

• incompressible Navier-Stokes equations
• regularity of weak solutions
• regularity criteria