Stability of gaseous stars in the non-isentropic case

The motion of the self-gravitational gaseous stars can be described by the Euler-Poisson equations. The main purpose of this article is concerned with the nonlinear stability of gaseous stars in the non-isentropic case, when is a smooth bounded function. First, we verify that the steady states are minimizers of the energy via concentration-compactness method; then using the variational approach we obtain the stability results of the non-isentropic flow.