Stabilization and stability for the spherically symmetric Navier–Stokes–Poisson system Original Research Article

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)p=p(ρ), we present global-in-time bounds for solutions with arbitrarily large data. For non-decreasing pp, the ωω-limit set for the density ρρ is studied. For increasing pp, 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.