Instability theory of the Navier-Stokes-Poisson equations

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 $6\mathrm{/}5<\gamma <4\mathrm{/}3$.