Nonlinear Asymptotic Stability of Gravitational Hydrostatic Equilibrium for Viscous White Dwarfs with Symmetric Perturbations

Abstract: We prove the nonlinear asymptotic stability of the gravitational hydrostatic equilibrium for the general equation of state of pressure-density relation in the framework of vacuum free boundary problem of spherically symmetric compressible Navier-Stokes-Poisson equations in three dimensions.The results apply to white dwarfs and polytropes with $\gamma\ge 2$, for which even the linearized asymptotic stability results are not available in literature, to the best of the authors' knowledge. Detailed decay rates of perturbations are given.