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 αα and ββ are suitably large. These results are some improvements of very recent work (Chae and Lee, 2014) established by Chae and Lee.