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

2026/07/31 by Han Cao
Mathematics · #math.AP

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arxiv created 2026/07/31 · arxiv updated 2026/08/03

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(ρ)=ρ^(4)/(3) and degenerate viscosity. It is well-known that linearly expanding GW solutions are special solutions to the Euler-Poisson system with γ=(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 ρ^α with 0<α≤(2)/(3) and zero bulk viscosity, we prove the nonlinear stability of linearly expanding GW solutions under radial perturbation.

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