A priori estimates of local solutions to compressible Navier-Stokes equations with free boundary (Q2011222)

The authors are concerned with the vacum free boundary problem of the compressible Navier-Stokes system in 2D. By using Lagrangian variables, they present a priori estimates of local-in-ime solutions in an appropriate Sobolev space. The main objetive of this article consists in the study of the physical vacuum free surface problem without imposing the symmetry condition. The strategy for handling such problems is nearly the same every time. It starts with the transition of the original domain having free boundaries to a fixed domain in Lagrangian coordinates. Then the considerations are realized in that domain. A lot of modern techniques come to an application. The paper is a very technical one. It is not easy to read such a paper because many estimates occcure througout the paper. The article under consideration contains 20 well choosen references that give a good survey on the state of the art.