GLOBAL SOLUTIONS TO 3D ISENTROPIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH FREE BOUNDARY

In this paper, we consider the free boundary value problem of 3D isentropic compressible Navier-Stokes equations with the stress free boundary condition where the compressible viscous flow of finite mass expands into infinite vacuum. The density changes continuously (or discontinuously) across the interfaces separating the fluid and vacuum. For the spherically symmetric initial data with finite energy, we prove the global existence of spherically symmetric weak solutions. Furthermore, we investigate the expanding rate of the domain occupied by the fluid.