On the global well-posedness for the compressible Hall-MHD system

Abstract

In this paper, we prove the global well-posedness of the Cauchy problem to the 3-D compressible Hall-magnetohydrodynamic (MHD) system supplemented with a class of large initial data in Besov spaces. By exploiting the intrinsic structure of the compressible Hall-MHD equations, we obtain the diffusion and the dispersive effects for the mixed hyperbolic-parabolic system. Based on this important observation, we prove that the compressible Hall-MHD system exists a global solution with the initial data close to a stable equilibrium.