Title: Finite Energy Compensated Compactness Method for Isentropic Gas Dynamics
Abstract: I will discuss the existence theory for the isentropic Euler equations of gas dynamics in a number of settings admitting symmetries. The use of these symmetries allows for the reduction of the system to a 1+1-dimensional problem (possibly with geometric source terms). I will describe a framework, based on the theory of compensate compactness, to allow for the treatment of existence and vanishing viscosity problems for solutions with finite energy to the Euler equations in such settings assuming physically reasonable equations of state. This is based on joint works with Gui-Qiang Chen and Simon Schulz.