Instability theory of the Navier-Stokes-Poisson equations

TL;DR

This paper investigates the stability of gaseous star models described by the Navier-Stokes-Poisson equations, establishing conditions under which these models are linearly and nonlinearly unstable for specific adiabatic exponents.

Contribution

It provides the first rigorous analysis of the dynamical instability of Lane-Emden star solutions within the Navier-Stokes-Poisson framework for certain adiabatic exponents.

Findings

Proves linear instability of Lane-Emden solutions for $6/5 < \, ext{γ} < 4/3$

Establishes nonlinear instability results for the same range of adiabatic exponents

Contributes to understanding astrophysical gaseous star stability in fluid dynamics models

Abstract

The stability question of the Lane-Emden stationary gaseous star configurations is an interesting problem arising in astrophysics. We establish both linear and nonlinear dynamical instability results for the Lane-Emden solutions in the framework of the Navier-Stokes-Poisson system with adiabatic exponent $6/5 < \gamma < 4/3$.