A quasi-one-dimensional Riemann problem for the isentropic gas dynamics equations

We consider a Riemann problem for the isentropic gas dynamics equations in two space dimensions modeling shock reflection. We write the problem in self-similar coordinates and, by analyzing a quasi-one-dimensional Riemann problem at the reflection point, we derive regimes, in terms of initial data, for which solutions model the phenomenon of regular shock reflection. This sets the stage for existence analysis of solutions to this Riemann problem using the approach by Canic, Keyfitz, Kim and Lieberman on the study of two-dimensional Riemann problems for systems of conservation laws.