Nonlinear Stability of Expanding Star Solutions of the Radially Symmetric Mass-Critical Euler-Poisson System
Nonlinear Stability of Expanding Star Solutions of the Radially Symmetric Mass-Critical Euler-Poisson System
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DOI：
10.1002/cpa.21721
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发表时间：
2018-05-01
影响因子：
3
通讯作者：
Jang, Juhi
中科院分区：
文献类型：
--
作者：
Hadzic, Mahir;Jang, Juhi
证明了质量临界引力Euler-Poisson系统的紧支集扩张星解的非线性稳定性。这些特殊的解是由Goldreich和Weber在1980年发现的。这种解的扩张率可以是自相似的，也可以是非自相似的(线性)，我们处理这两种类型。我们稳定性结果的一个重要结果是存在一类新的全局时间径向对称解，它们不是同源的，因此不包含在现有的工作中。利用拉格朗日坐标，我们将相关的自由边界问题转化为紧空间区域上的退化拟线性波动方程。对于不变重标度，该问题是质量临界的，并且分析是在相似变量中进行的。(C)2017威利期刊公司。
We prove nonlinear stability of compactly supported expanding star solutions of the mass-critical gravitational Euler-Poisson system. These special solutions were discovered by Goldreich and Weber in 1980. The expansion rate of such solutions can be either self-similar or non-self-similar (linear), and we treat both types. An important outcome of our stability results is the existence of a new class of global-in-time radially symmetric solutions, which are not homologous and therefore not encompassed by the existing works. Using Lagrangian coordinates we reformulate the associated free-boundary problem as a degenerate quasilinear wave equation on a compact spatial domain. The problem is mass-critical with respect to an invariant rescaling and the analysis is carried out in similarity variables. (c) 2017 Wiley Periodicals, Inc.