Regularity criteria and small data global existence to the generalized viscous Hall-magnetohydrodynamics

In this paper we establish the regularity criteria of solutions to the three space dimensions generalized viscous Hall-magnetohydrodynamics. Moreover, we also prove that there exist classical solutions globally in time to the generalized viscous Hall-MHD if the initial data is small enough or the fractional Laplacian dissipation powers α and β are suitably large. These results are some improvements of very recent work (Chae and Lee, 2014) established by Chae and Lee.