REGULARITY CRITERIA FOR THE 3D MHD EQUATIONS VIA PARTIAL DERIVATIVES

In this paper, we establish two regularity criteria for the 3D MHD equations in terms of partial derivatives of the velocity field or the pressure. It is proved that if partial derivative(3)u is an element of L-beta(0, T; L-alpha(R-3)), with 2/beta + 3/alpha <= 3(alpha+2)/4 alpha, alpha > 2, or del P-h is an element of L-beta(0, T; L-alpha(R-3)), with 2/beta + 3/alpha < 3, alpha > 9/7, beta >= 1, then the weak solution (u, b) is regular on [0, T].