On the dynamics of Navier-Stokes equations for a spherically symmetric shallow water model

In this paper, we study a free boundary value problem for the spherically symmetric compressible Navier-Stokes system with degenerate viscosity coefficients, which include, in particular, a shallow water model. We obtain global existence, uniqueness and large time behavior of weak solutions under some assumptions imposed on initial data. In particular, the results show that such a system is stable for small initial general perturbations.