# American Institute of Mathematical Sciences

March  2017, 22(2): 537-567. doi: 10.3934/dcdsb.2017026

## Global classical solutions to the free boundary problem of planar full magnetohydrodynamic equations with large initial data

 Department of Mathematics, School of Information, Renmin University of China, Beijing 100872, China

* Corresponding author

Received  March 2016 Revised  June 2016 Published  December 2016

The free boundary problem of planar full compressible magnetohydrodynamic equations with large initial data is studied in this paper, when the initial density connects to vacuum smoothly. The global existence and uniqueness of classical solutions are established, and the expanding rate of the free interface is shown. Using the method of Lagrangian particle path, we derive some L estimates and weighted energy estimates, which lead to the global existence of classical solutions. The main difficulty of this problem is the degeneracy of the system near the free boundary, while previous results (cf. [4,30]) require that the density is bounded from below by a positive constant.

Citation: Yaobin Ou, Pan Shi. Global classical solutions to the free boundary problem of planar full magnetohydrodynamic equations with large initial data. Discrete & Continuous Dynamical Systems - B, 2017, 22 (2) : 537-567. doi: 10.3934/dcdsb.2017026
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