修正的星系动力学中的各向同性定态
Isotropic steady states in galactic dynamics revised
摘要：
本文完成了我们早先关于恒星动力学情形下Vlasov-Poisson系统定态解的非线性稳定性的结果。通过在质量-Casimir约束下极小化能量，我们构造了一大类各向同性球对称定态，并证明了它们对一般情形的非线性稳定性。例如，不一定是对称扰动。在某种意义上，这类是最优的，特别是，它包含了所有有限质量的多面体，并且对粒子能量的依赖性逐渐减小。
英文摘要：
The present 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.
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