Expanding Solutions to Free Boundary 3D Spherically Symmetric Compressible Navier-Stokes-Poisson Equations near the Lane-Emden Stars

2025/11/23 by Cao, Han · 1 citation
Earth and Planetary Sciences · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations #Ocean Waves and Remote Sensing

paper · doi:10.48550/arxiv.2511.18339

openalex publication_date 2025/11/23 · openalex created_date 2025/11/27 · openalex updated_date 2026/07/28

Abstract

We consider the gravitational Navier-Stokes-Poisson equations with the equation of state P(ρ)=Kρ^γ, where γ∈((6)/(5),(4)/(3)], which models the viscous polytropic gaseous stars. We prove the existence of global weak solutions to the equations with constant viscosity and radially symmetric initial data. For γ=(4)/(3), we require the initial data having mass less than the mass of the Lane-Emden stars; for γ∈((6)/(5),(4)/(3)), we require that the initial data belong to an invariant set where initial initial data can be taken near the Lane-Emden stars. For γ∈((6)/(5),(4)/(3)), we show that the invariant set contains some initial data that are not allowed in previous literature. We also prove the support of any strong solution expands to infinity for the Navier-Stokes-Poisson equations with constant viscosity and a class of density-dependent viscosity, which indicates the strong instability of Lane-Emden solutions for the Navier-Stokes-Poisson equations.

Citations

• Expanding solutions near unstable Lane-Emden stars
• Nonlinear stability of non-rotating gaseous stars
• Turning point principle for stability of viscous gaseous stars
• Global Solutions of the Compressible Euler-Poisson Equations with Large Initial Data of Spherical Symmetry
• Separable Hamiltonian PDEs and Turning point principle for stability of gaseous stars
• A Model of Radiational Gaseous Stars
• Nonlinear stability of expanding star solutions in the radially-symmetric mass-critical Euler-Poisson system
• On Nonlinear Asymptotic Stability of the Lane-Emden Solutions for the Viscous Gaseous Star Problem
• Nonlinear Instability Theory of Lane-Emden stars
• Instability theory of the Navier-Stokes-Poisson equations
• Local Well-Posedness of Dynamics of Viscous Gaseous Stars

Cited by

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

Related

• On Nonlinear Asymptotic Stability of the Lane-Emden Solutions for the Viscous Gaseous Star Problem
• Expanding solutions near unstable Lane-Emden stars
• Global Solutions of the Compressible Euler-Poisson Equations with Large Initial Data of Spherical Symmetry
• Local Well-Posedness of Dynamics of Viscous Gaseous Stars
• Instability theory of the Navier-Stokes-Poisson equations