Regularity criteria for the 3D MHD equations involving partial components

In this paper, we establish two new regularity criteria for the 3D incompressible MHD equations involving partial components of the velocity and magnetic fields. It is proved that if u(3), b is an element of L(alpha)(0, T ; L(gamma)(R(3))), 2/alpha + 3/gamma <= 3/4 + 1/2 gamma, gamma > 10/3 or u(3), b is an element of L(alpha 1) (0, T ; L(gamma 1) (R(3))), with 2/alpha(1) + 3/gamma(1) <= 1, 3 < gamma(1) <= infinity, partial derivative(3)u(1), partial derivative(3)u(2) is an element of L(alpha 2) (0, T ; L(gamma 2)(R(3))), with 2/alpha(2) + 3/gamma(2) <= 2, 3/2 < gamma(2) <= infinity, then the local strong solution (u, b) remains smooth on [0, T]. (C) 2011 Elsevier Ltd. All rights reserved.