# American Institute of Mathematical Sciences

October  2019, 24(10): 5503-5522. doi: 10.3934/dcdsb.2019068

## Low Mach number limit of strong solutions for 3-D full compressible MHD equations with Dirichlet boundary condition

 1 School of Mathematical Sciences, Peking University, Beijing 100871, China 2 Institute of Applied Physics and Computational Mathematics, Beijing, 100088, China

* Corresponding author: Lan Zeng

Received  June 2018 Revised  October 2018 Published  October 2019 Early access  April 2019

Fund Project: The second author is supported by Science Challenge Project, No.TZ2016002.

In this paper, we consider the low Mach number limit of the full compressible MHD equations in a 3-D bounded domain with Dirichlet boundary condition for velocity field, Neumann boundary condition for temperature and perfectly conducting boundary condition for magnetic field. First, the uniform estimates in the Mach number for the strong solutions are obtained in a short time interval, provided that the initial density and temperature are close to the constant states. Then, we prove the solutions of the full compressible MHD equations converge to the isentropic incompressible MHD equations as the Mach number tends to zero.

Citation: Lan Zeng, Guoxi Ni, Yingying Li. Low Mach number limit of strong solutions for 3-D full compressible MHD equations with Dirichlet boundary condition. Discrete & Continuous Dynamical Systems - B, 2019, 24 (10) : 5503-5522. doi: 10.3934/dcdsb.2019068
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