气态星的非线性稳定性
Non-linear stability of gaseous stars
摘要：
我们构造的欧拉-泊松系统的正压状态方程作为一个适当定义的能量泛函的最小值的定常状态。它们的最小化性质意味着这种状态对一般的非线性稳定性，即，不一定是球对称扰动。数学方法是基于以前的Vlasov-Poisson系统的稳定性结果Y。利用能量-Casimir技术。分析是有条件的，在这个意义上，它假设存在的解决方案，保持质量和能量的Euler-Poisson系统的初值问题。在此背景下，Euler-Poisson和Vlasov-Poisson系统之间的关系也进行了探讨。
英文摘要：
We construct steady states of the Euler-Poisson system with a barotropic equation of state as minimizers of a suitably defined energy functional. Their minimizing property implies the non-linear stability of such states against general, i.e., not necessarily spherically symmetric perturbations. The mathematical approach is based on previous stability results for the Vlasov-Poisson system by Y. Guo and the author, exploiting the energy-Casimir technique. The analysis is conditional in the sense that it assumes the existence of solutions to the initial value problem for the Euler-Poisson system which preserve mass and energy. The relation between the Euler-Poisson and the Vlasov-Poisson system in this context is also explored.
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