Existence and conditional nonlinear stability of non-isentropic gaseous stars

The motion of self-gravitating gaseous stars with non-isentropic effects can be described by the non-isentropic Euler–Poisson equations. Using a variational approach, we establish the existence of steady-state solutions for prescribed total mass, under a fixed relation between the mass and entropy distributions. We provide the decay rate of the density near the vacuum boundary. Finally, assuming the existence of a radial weak solution satisfying the stated Lagrangian and compatibility conditions, nonincrease of the total energy, and uniqueness of the variational minimizer, we prove a conditional nonlinear stability result under radial perturbations.