Global existence of weak solution for the compressible Navier–Stokes–Poisson system for gaseous stars

We study the multi-dimensional compressible Navier–Stokes–Poisson system with γ  -law pressure and density-dependent viscosity coefficients in the simulation of the motion of gaseous stars. The global existence of spherically symmetric weak solutions to the free boundary value problem for the Navier–Stokes–Poisson system for γ∈(65,43] is shown for arbitrarily large initial data with compact support.