Noble-Abel gas diffusion at convex corners of the two-dimensional compressible magnetohydrodynamic system

Abstract

In this paper, we study the expansion of Noble-Abel gas into a vacuum around the convex corner of the two-dimensional compressible magnetohydrodynamic system. We reduce this problem to the interaction of a centered simple wave emanating from the convex corner with a backward planar simple wave. Mathematically, this is a Goursat problem. By using the method of characteristic decomposition and construction of invariant regions, combining $ C^{0} $ and $ C^{1} $ estimation as well as hyperbolicity estimation, we obtain the existence of a global classical solution by extending the local classical solution.

Keywords

• gas diffusion
• convex corner
• compressible magnetohydrodynamic system
• noble-able gas
• goursat problem