Remarks on the regularity criterion to the Navier-Stokes equations via the gradient of one velocity component

摘要

In this paper, we consider the classical three-dimensional (3D) incompressible Navier-Stokes equations. By making use of a new anisotropic Sobolev inequality, we improve a regularity criterion for the weak solution to the 3D Navier-Stokes equations involving the gradient of one velocity component. This result improves the previous work of Zhou and Pokorny (2010). (C) 2015 Elsevier Inc. All rights reserved.