恒星动力学中的平坦定态-存在性和稳定性
Flat steady states in stellar dynamics - existence and stability
摘要：
我们考虑一个特殊情况下的三维弗拉索夫-泊松系统的粒子被限制在一个平面上，在天体物理学中使用的模型非常扁平的星系的情况。我们证明了该系统平衡态的存在性。它们是作为能量-Casimir泛函的极小值而获得的，从这一事实中推导出一定的动力学稳定性。从数学的角度来看，这些稳定状态提供了三维Vlasov-Poisson系统的部分奇异解的例子。
英文摘要：
We consider a special case of the three dimensional Vlasov-Poisson system where the particles are restricted to a plane, a situation that is used in astrophysics to model extremely flattened galaxies. We prove the existence of steady states of this system. They are obtained as minimizers of an energy-Casimir functional from which fact a certain dynamical stability property is deduced. From a mathematics point of view these steady states provide examples of partially singular solutions of the three dimensional Vlasov-Poisson system.
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