On global existence, energy decay and blow-up criteria for the Hall-MHD system

In this paper, we obtain global existence and energy decay for 3D Hall-magnetohydrodynamics (Hall-MHD) system with Ait and AB. Besides the classical energy method and Besov space techniques, the interpolating inequalities are crucial in the proof of decay estimates. Then two Osgood type blow-up criteria are established. Our results improve the corresponding theorems in 3 and M. In addition, we establish two Beale Kato Majda blow-up criterion for the generalized version of Hall-MHD with -Delta u and (-Delta)beta B, beta>1. (C) 2015 Elsevier Inc. All rights reserved.