Regularity via one vorticity component for the 3D axisymmetric MHD equations

Abstract

In this paper, we investigate the regularity criteria of axisymmetric weak solutions to the three-dimensional (3D) incompressible magnetohydrodynamics (MHD) equations with nonzero swirl component. By making use of techniques of the Littlewood-Paley decomposition, we show that weak solutions to the 3D axisymmetric MHD equations become regular if the swirl component of vortic-) , which partially gives a positive answer to the marginal case for the regularity of MHD equations.