#### Vol. 6, No. 5, 2013

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Instability theory of the Navier–Stokes–Poisson equations

### Juhi Jang and Ian Tice

Vol. 6 (2013), No. 5, 1121–1181
##### 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 $\frac{6}{5}<\gamma <\frac{4}{3}$.

##### Keywords
Navier–Stokes–Poisson, free boundary problems, gaseous stars, hydrodynamic instability, nonlinear instability
##### Mathematical Subject Classification 2010
Primary: 35Q30, 35R35, 76E20, 85A30