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arXiv · 2607.28960

Nonlinear Stability of Linearly Expanding Goldreich-Weber Solutions for the Navier-Stokes-Poisson System with Degenerate Viscosity Under Radial Perturbations

Han Cao
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Abstract

In this work, we study the nonlinear stability of linearly expanding Goldreich-Weber (GW) solutions for the gravitational Navier-Stokes-Poisson system with pressure law $p(\rho)=\rho^{\frac{4}{3}}$ and degenerate viscosity. It is well known that linearly expanding GW solutions are special solutions to the Euler-Poisson system with $\gamma=\frac{4}{3}$. With bulk viscosity equal to 0, linearly expanding GW solutions are also solutions to the Navier-Stokes-Poisson equations. Choosing shear viscosity proportional to $\rho^{\alpha}$ with $0<\alpha\le\frac{2}{3}$ and zero bulk viscosity, we prove the nonlinear stability of linearly expanding GW solutions under radial perturbations.

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Han Cao. 2026-07-31. Nonlinear Stability of Linearly Expanding Goldreich-Weber Solutions for the Navier-Stokes-Poisson System with Degenerate Viscosity Under Radial Perturbations. https://arxiv.org/abs/2607.28960

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