恒星动力学中的稳定定态
Stable steady states in stellar dynamics
摘要：
在恒星动力学情形下，证明了Vlasov-Poisson系统定态的存在性和非线性稳定性。得到的稳定状态的能量卡西米尔功能的最小值，从事实推导出他们的动力学稳定性。该分析适用于一些著名的多变的稳定状态，但它也大大扩展了类已知的稳定状态。
英文摘要：
We prove the existence and nonlinear stability of steady states of the Vlasov-Poisson system in the stellar dynamics case. The steady states are obtained as minimizers of an energy-Casimir functional from which fact their dynamical stability is deduced. The analysis applies to some of the well-known polytropic steady states, but it also considerably extends the class of known steady states.
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