Global Behavior of Spherically Symmetric Navier-Stokes-Poisson System with Degenerate Viscosity Coefficients

摘要

In this paper, we study a free boundary problem for compressible spherically symmetric Navier-Stokes-Poisson equations with degenerate viscosity coefficients and without a solid core. Under certain assumptions that are imposed on the initial data, we obtain the global existence and uniqueness of the weak solution and give some uniform bounds (with respect to time) of the solution. Moreover, we obtain some stabilization rate estimates of the solution. The results show that such a system is stable under small perturbations, and could be applied to the astrophysics.