Abstract
In this paper, regularity criterion for the 3-D density-dependent magnetohydrodynamic equation is considered. It is proved that the solution keeps smoothness only under an integrable condition on the velocity field in multiplier spaces. Hence, it turns out that the velocity field plays a dominant role in the regularity criteria of the weak solutions to this nonlinear coupling problem even with density. Copyright (C) 2009 John Wiley & Sons, Ltd.