Non-Linear Stability of Gaseous Stars
Non-Linear Stability of Gaseous Stars
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DOI：
10.1007/s00205-003-0260-y
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发表时间：
2002-10
影响因子：
2.5
通讯作者：
G. Rein
中科院分区：
文献类型：
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作者：
G. Rein
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，不一定是球对称的扰动。数学方法是基于以前的Vlasov-Poisson系统的稳定性结果Y。Guo和G. Rein，利用能量-卡西米尔技术。该分析是有条件的，在这个意义上，它证明了存在的解决方案的初始值问题的Euler-Poisson系统，保持质量和能量。在此背景下，Euler-Poisson和Vlasov-Poisson系统之间的关系也进行了探讨。
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 G. Rein, exploiting the energy-Casimir technique. The analysis is conditional in the sense that itassumesthe 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.