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

Abstract

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.