Zoom link: https://princeton.zoom.us/j/9148065146

Since the seminal work of Tartar and DiPerna, the method of compensated compactness has been a valuable tool for proving the existence of entropy solutions to certain 1D models of the isentropic gas dynamics. In this talk, I will outline the finite energy modification of this strategy, which is designed to provide such an existence framework even when we cannot hope for uniform L^\infty bounds on the solution. I will discuss the application of this method to the vanishing physical viscosity limit from the 1D compressible Navier-Stokes equations, as well as the transonic nozzle problem and the spherically symmetric Euler equations. These results are joint work with Gui-Qiang Chen and Simon Schulz.