Vacuum states for compressible flow

In this paper we study the evolutions of the interfaces betweengases and the vacuum for both inviscid and viscous one dimensionalisentropic gas motions. The local (in time) existence of solutionsfor both inviscid and viscous models with initial data containingvacuum states is proved and some singular properties on the freesurfaces separating the gas and the vacuum are obtained. It isfound that the Euler equations are better behaved near the vacuum thanthe compressible Navier-Stokes equations. The Navier-Stokesequations with viscosity depending on density are introduced, which is shown to be well-posed (at leastlocally) and yield the desired solutions near vacuum.