Shock Reflection Problems and Gas Dynamics Equations

We present mathematical analysis of shock reflection phenomenon using two-dimensional systems of conservation laws. Depending on the initial data, various types of shock reflection are possible, such as regular reflection (either supersonic or transonic) or Mach. We present proof of existence of regular reflection for the system of isentropic gas dynamics equations. The main idea in our approach is to rewrite the system using the self-similar coordinates. This leads to a free boundary problem for the subsonic state and the reflected shock. Existence of a solution is proved using the Holder estimates for the second order elliptic equations and various fixed point arguments. This work is joint with Barbara Lee Keyfitz (Ohio State University) and Suncica Canic (University of Houston).