A regularity criterion of smooth solution for the 3D viscous Hall-MHD equations

In this work, we investigate the regularity criterion for the solution of the Hall-MHD system in three-dimensions. It is proved that if the pressure pi and the gradient of magnetic field del B satisfies some kind of space-time integrable condition on [0, T], then the corresponding solution keeps smoothness up to time T. This result improves some previous works to the Morrey space M-2,M- 3/r for 0 <= r < 1 which is larger than L-3/r.