Free boundary value problem to 3D spherically symmetric compressible Navier-Stokes-Poisson equations

TL;DR

This paper proves the global existence and analyzes the long-term behavior of spherically symmetric weak solutions to the 3D compressible Navier-Stokes-Poisson equations modeling self-gravitating gaseous stars with free boundary conditions.

Contribution

It establishes the global existence of weak solutions and investigates their regularity and long-time behavior under specific boundary and initial conditions.

Findings

Global weak solutions exist for certain initial data.

Solutions exhibit specific regularity and decay properties.

Results depend on the total mass being below a critical threshold.

Abstract

In the paper, we consider the free boundary value problem to 3D spherically symmetric compressible isentropic Navier-Stokes-Poisson equations for self-gravitating gaseous stars with $\gamma$-law pressure density function for $6/5 <\gamma \leq 4/3$. For stress free boundary condition and zero flow density continuously across the free boundary, the global existence of spherically symmetric weak solutions is shown, and the regularity and long time behavior of global solution are investigated for spherically symmetric initial data with the total mass smaller than a critical mass.