×

Isotropic steady states in galactic dynamics. (English) Zbl 0974.35093

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.

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
PDFBibTeX XMLCite
Full Text: DOI arXiv