Existence and non-linear stability of rotating star solutions of the compressible euler-poisson equations

We prove the existence of rotating star solutions which are steady-state solutions of the compressible isentropic Euler-Poisson (Euler-Poisson) equations in three spatial dimensions with prescribed angular momentum and total mass. This problem can be formulated as a variational problem of finding a minimizer of an energy functional in a broader class of functions having less symmetry than those functions considered in the classical Auchmuty-Beals paper. We prove the non-linear dynamical stability of these solutions with perturbations having the same total mass and symmetry as the rotating star solution. We also prove finite time stability of W^1,∞(ℝ³) solutions where the perturbations are entropy-weak solutions of the Euler-Poisson equations. Finally, we give a uniform (in time) a priori estimate for entropy-weak solutions of the Euler-Poisson equations. © 2008 Springer-Verlag.