Guo, Yan; Rein, Gerhard Isotropic steady states in galactic dynamics. (English) Zbl 0974.35093 Commun. Math. Phys. 219, No. 3, 607-629 (2001). Summary: The paper completes our earlier results on nonlinear stability of stationary solutions of the Vlasov-Poisson system in the stellar dynamics case. By minimizing the energy under a mass-Casimir constraint we construct a large class of isotropic, spherically symmetric steady states and prove their nonlinear stability against general, i.e., not necessarily symmetric perturbations. The class is optimal in a certain sense, in particular, it includes all polytropes of finite mass with decreasing dependence on the particle energy. Cited in 3 ReviewsCited in 45 Documents MSC: 35Q35 PDEs in connection with fluid mechanics 85A05 Galactic and stellar dynamics 76X05 Ionized gas flow in electromagnetic fields; plasmic flow 35B35 Stability in context of PDEs Keywords:nonlinear stability of stationary solutions of the Vlasov-Poisson system; stellar dynamics; minimizing the energy under a mass-Casimir constraint PDFBibTeX XMLCite \textit{Y. Guo} and \textit{G. Rein}, Commun. Math. Phys. 219, No. 3, 607--629 (2001; Zbl 0974.35093) Full Text: DOI arXiv