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

TL;DR

This paper proves the nonlinear asymptotic stability of gravitational hydrostatic equilibrium in white dwarfs with symmetric perturbations, providing detailed decay rates and extending stability results to cases where linear analysis is lacking.

Contribution

It establishes the nonlinear stability of white dwarf models with general equations of state for the first time, including cases with no prior linear stability results.

Findings

Proves nonlinear asymptotic stability for white dwarfs with γ ≥ 2.

Provides explicit decay rates of perturbations.

Extends stability analysis to cases lacking linear results.

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.