Some new regularity criteria for the 3D MHD equations

In this paper we consider the regularity criteria for solutions to the 3D incompressible magnetohydrodynamics (MFID) equations. The first one involves del(h)u = (partial derivative(1)u, partial derivative(2)u) and partial derivative(3)b. Then, the criterion concerning del(h)u and del(h)b = (partial derivative(1)b, partial derivative(2)b) is presented. Finally, we show that the weak solution (u, b) is actually regular, provided that u(3), partial derivative(3)u, b and partial derivative(3)b are in suitable Serrin-type integrability classes, respectively. (C) 2012 Elsevier Inc. All rights reserved.