A Regularity Criterion for the 3D Density-Dependent MHD Equations

In this paper, we consider the 3D density-dependent magnetohydrodynamic equations with vacuum in the whole space $$\mathbb {R}^{3}$$, and provide a regularity criterion involving the velocity field in BMO space norm. This work generalizes the regularity criterion of the constant density MHD equations to the density-dependent one.