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 −Δu and −ΔB. 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 [4]. In addition, we establish two Beale-Kato-Majda blow-up criterion for the generalized version of Hall-MHD with −Δu and (−Δ)βB, β>1.