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On nonlinear stability of polytropic galaxies. (English) Zbl 0927.70019
Summary: We consider a certain class of stationary solutions of the Vlasov-Poisson system with a Newtonian potential. These solutions represent some spherically-symmetric, rotating galaxies obeying the generalized Emden-Fowler law. A nonlinear stability under spherically symmetric perturbations is proved. The proof is based on an adaptation of the energy-Casimir method, which implies a uniform estimate on the mass distribution of the perturbed solutions.

70K20 Stability for nonlinear problems in mechanics
85A05 Galactic and stellar dynamics
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