Global Well-Posedness and Incompressible Limit of the Hall-Magnetohydrodynamic System in a Bounded Domain

Abstract

In this paper we firstly prove the global well-posedness for the compressible Hall-magnetohydrodynamic system in a bounded domain when the initial data is small. On this basis, we continue to study the convergence of the corresponding equations with the well-prepared initial data as the Mach number tends to zero.