Expansion of gas by turning a sharp corner into vacuum for 2-D pseudo-steady compressible magnetohydrodynamics system

Abstract

This paper is concerned with the process of a gas expanding into vacuum by turning around a sharp corner for 2-D pseudo-steady compressible magnetohydrodynamics system. This problem actually can be interpreted as interaction of a centered wave and a planar rarefaction wave. As the gas touches the corner and starts expanding into the vacuum around the sharp corner, a centered wave and a planar rarefaction wave appear. In the estimates of solution, we utilize the characteristic analysis and deduce proper characteristic decompositions. Combining the C0 estimate, gradient estimates, hyperbolicity, and the interaction of centered wave and planar rarefaction wave, we constructively obtain the existence of global classical solution to the present problem.