Regularity criteria for the Navier-Stokes equations based on one or two items of the velocity gradient

摘要

We study the regularity criteria for the incompressible Navier-Stokes equations based on either one item of the velocity gradient, partial derivative(1)u(3) or partial derivative(3)u(3) or on two items of the velocity gradient, partial derivative(2)u(3), partial derivative(3)u(3), or partial derivative(1)u(3), partial derivative(2)u(3). We improve and/or extend several results from the literature by the use of two versions of the generalized Troisi inequality. (C) 2017 Elsevier Ltd. All rights reserved.