Stability of rarefaction wave for steady supersonic relativistic Euler flows past Lipschitz wedges

Abstract

This paper is devoted to studying two-dimensional steady supersonic relativistic Euler flows past a sharp corner or a bending wedge. When the vertex angle is larger than π and the wedge is a small perturbation of a convex rigid wall, we prove the global existence and stability of entropy solution including a large rarefaction wave under some small perturbations of the initial data and the slope of the boundary. Moreover, we obtain global non-relativistic limits of entropy solution as well as the asymptotic behavior of the solution as $x\to +\infty$.