发表机构
University of Southern California（南加州大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对带退化黏性的引力纳维-斯托克斯-泊松系统，在特定剪切黏性条件下，证明了线性膨胀Goldreich-Weber解在径向扰动下的非线性稳定性。
AI 中文摘要
本研究针对带压强律 $p(\rho)=\rho^{\frac{4}{3}}$ 和退化黏性的引力纳维-斯托克斯-泊松系统，探讨线性膨胀Goldreich-Weber（GW）解的非线性稳定性。已知线性膨胀GW解是 $\gamma=\frac{4}{3}$ 时欧拉-泊松系统的特殊解，当体积黏性为0时，线性膨胀GW解也是纳维-斯托克斯-泊松方程的解。选取剪切黏性与 $\rho^{\alpha}$ 成正比（$0<\alpha\le\frac{2}{3}$）且体积黏性为0的条件，证明线性膨胀GW解在径向扰动下的非线性稳定性。
英文摘要
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 $p(ρ)=ρ^{\frac{4}{3}}$ and degenerate viscosity. It is well known that linearly expanding GW solutions are special solutions to the Euler-Poisson system with $γ=\frac{4}{3}$. With bulk viscosity equal to 0, linearly expanding GW solutions are also solutions to the Navier-Stokes-Poisson equations. Choosing shear viscosity proportional to $ρ^α$ with $0<α\le\frac{2}{3}$ and zero bulk viscosity, we prove the nonlinear stability of linearly expanding GW solutions under radial perturbations.
