Stabilization and stability for the spherically symmetric Navier-Stokes-Poisson system

We consider global behaviour of viscous compressible flows with spherical symmetry driven by gravitation and an outer pressure, outside a hard core. For a general state function p=p(ρ), we present global-in-time bounds for solutions with arbitrarily large data. For non-decreasing p, the ω-limit set for the density ρ is studied. For increasing p, uniqueness and static stability of the stationary solutions (including variational aspects) are investigated. Moreover, stabilization rate bounds toward the statically stable solutions are given and their nonlinear dynamical stability is shown.