Abstract
We prove that a weak solution (u, b) to the MHD equations is smooth on (0, T] if M is an element of L-alpha (0, T; L-gamma (R-3)) with 2/alpha + 3/gamma = 2, 1 <= alpha < infinity and 3/2 < gamma <= infinity, where M is a 3 x 3 mixture matrix (see its definition below). As we will explain later, this kind of regularity criteria is more likely to capture the nature of the coupling effects between the fluid velocity and the magnetic field in the evolution of the MHD flows. Moreover, the condition on M is scaling invariant, i.e. it is of Ladyzhenskaya-Prodi-Serrin type.