Steady Supersonic Flows Past Lipschitz Wedges for Two-Dimensional Relativistic Euler Equations

SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 5474-5520, August 2024.
Abstract. We are concerned with two-dimensional steady supersonic flows past Lipschitz wedges for the relativistic Euler equations. If the vertex angle of the upstream flow is less than the critical angle, determined by shock polar, then a shock wave is generated from the wedge vertex. When the total variations of the tangent angle of the boundary and the upstream flow are both suitably small, we establish global stability of entropy solutions, including a large 1-shock wave. Moreover, we obtain global nonrelativistic limits of the entropy solutions, and also investigate the asymptotic behavior of these solutions as [math]. It is worth mentioning that we demonstrate the basic properties of nonlinear waves for the two-dimensional steady relativistic Euler system, especially the geometric structure of shock polar.