Free Boundary Problems for Compressible Flows

The macroscopic dynamics of compressible gasses and fluids are well described by the compressible Euler and Navier Stokes equations. In the simplest setting, these equations track the evolution of the gas density and velocity as a coupled system. In these notes we consider the physical situation where the gas or fluid is bordered by a vacuum region with a freely moving boundary, with the density approaching zero near the vacuum region. We refer to such combined evolutions as free boundary problems.