Low Mach number and non-resistive limit of magnetohydrodynamic equations with large temperature variations in general bounded domains

Abstract

This article verifies the low Mach number and non-resistive limit of local strong solutions to non-isentropic compressible magnetohydrodynamic (MHD) equations in general three-dimensional bounded domains when the temperature variation is large but finite. The uniform estimates of strong solutions are obtained in a short time interval independent of the Mach number and the magnetic resistivity coefficient, provided that the initial data are well prepared. Previous results on this multi-scale singular limit of compressible MHD equations are either for the cases of the weak solutions or for the cases of small temperature variations or for the cases of flat boundary where the mechanisms are essentially different. The new ingredient of this article is that we develop a new approach of weighted energy to establish the uniform estimates for high-order spatial derivatives of solutions.

Keywords

• low mach number limit
• non-resistive limit
• large temperature variations
• magnetohydrodynamic equations
• 35b40
• 35m33
• 35q35
• 76w05