Regularity criteria for the 3D MHD equations involving one current density and the gradient of one velocity component

摘要

In this paper, we consider the Cauchy problem for the 3D MHD equations, and provide a regularity criterion involving del u(3) and j(3), where u(3) and j(3) are the third component of the velocity and the current density, respectively. As by-products, we show that assumptions on two vorticity and one current density component are enough to ensure the smoothness of the solution, and improve some previous results (Skalak, 2014; Zhou and Pokorny, 2009, 2010) for the Navier-Stokes equations. (C) 2014 Elsevier Ltd. All rights reserved.