Global entropy solutions for compressible, isentropic Euler equations with geometric effects

I will discuss the application of the method of compensated compactness to the compressible, isentropic Euler equations under certain geometric assumptions, e.g. the case of fluid flow in a nozzle of varying cross-sectional area or the assumption of planar symmetry under special relativity. Under these assumptions, the equations reduce to the classical (or relativistic) one-dimensional isentropic Euler equations with additional geometric source terms. In this talk, I will explain how the classical strategy of DiPerna, Chen et. al. can be adapted to handle these more complicated systems and will highlight some of the difficulties involved in extending the techniques to the relativistic setting.