Regularity criteria for the 3D MHD equations in terms of the pressure

In this paper we consider the regularity criteria for weak solutions to the 3D MHD equations. It is proved that under the condition b being in the Serrin's regularity class, if the pressure p belongs to L-alpha,L-gamma with + 2/alpha + 3/gamma <= 2 or the gradient field of pressure del p belongs to L-alpha,L-gamma with 2/alpha + 3/gamma <= on [0, T], then the solution remains smooth on [0, T]. (c) 2007 Elsevier Ltd. All rights reserved.