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

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.