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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(ρ)=ρ4/3 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 ρα with 0<α≤2/3 and zero bulk viscosity, we prove the nonlinear stability of linearly expanding GW solutions under radial perturbations.

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Cite

BibTeXRIS
BibTeX
@misc{cao2026nonlinear,
  title = {{Nonlinear Stability of Linearly Expanding Goldreich-Weber Solutions for the Navier-Stokes-Poisson System with Degenerate Viscosity Under Radial Perturbations}},
  author = {Han Cao},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.28960},
  eprint = {2607.28960},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.28960},
}
RIS
TY  - UNPB
TI  - Nonlinear Stability of Linearly Expanding Goldreich-Weber Solutions for the Navier-Stokes-Poisson System with Degenerate Viscosity Under Radial Perturbations
AU  - Han Cao
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2607.28960
UR  - https://arxiv.org/abs/2607.28960
AB  - 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 perturbations.
ER  -