Low Mach number limit of the full compressible Hall-magnetohydrodynamic equation with general initial data

Abstract

In this paper, we are concerned with the low Mach number limit for the full compressible Hall-magnetohydrodynamic equations within the frame work of local smooth solution in R3. Under the assumption of large temperature variations, we first obtain the uniform estimates of the solutions in a ε-weighted Sobolev space, which establishes the local existence theorem of the full compressible Hall-magnetohydrodynamic equations on a finite time interval independent of the Mach number. Then, the low Mach limit is proved by combining the uniform estimates and the dispersive estimates on the wave equation due to Métivier and Schochet (2001).