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We prove existence of rotating star solutions which are steady-statesolutions of the compressible isentropic Euler-Poisson (EP) equations in 3spatial dimensions, with prescribed angular momentum and total mass. Thisproblem can be formulated as a variational problem of finding a minimizer of anenergy functional in a broader class of functions having less symmetry thanthose functions considered in the classical Auchmuty-Beals paper. We prove thenonlinear dynamical stability of these solutions with perturbations having thesame total mass and symmetry as the rotating star solution. We also prove localin time stability of $W^{1, \infty}(\RR^3)$ solutions where the perturbationsare entropy-weak solutions of the EP equations. Finally, we give a uniform (intime) a-priori estimate for entropy-weak solutions of the EP equations

Existence and Non-linear Stability of Rotating Star Solutions of the Compressible Euler–Poisson Equations