Instability theory of the Navier–Stokes–Poisson equations

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 $\frac{6}{5}<\gamma <\frac{4}{3}$.