A regularity criterion of smooth solution for the 3D viscous Hall-MHD equations - A. M. Alghamdi; S. Gala; M. A. Ragusa (AIMS Mathematics, 2018)
In this work, we investigate the regularitycriterion for the solution of the Hall-MHD system in three-dimensions. It isproved that if the pressure $π $ and the gradient of magnetic field $%\nabla B$ satisfies some kind of space-time integrable condition on $[0,T]$,then the corresponding solution keeps smoothness up to time $T$. This resultimproves some previous works to the Morrey space $\overset{· }{\mathcal{M}}_{2,\frac{3}{r}}$ for $0≤ r<1$ which is larger than $L^{\frac{3}{r}}$.