Separable Hamiltonian PDEs and Turning Point Principle for Stability of Gaseous Stars
Separable Hamiltonian PDEs and Turning Point Principle for Stability of Gaseous Stars
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DOI：
10.1002/cpa.22027
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发表时间：
2020-05
影响因子：
3
通讯作者：
Zhiwu Lin;C. Zeng
中科院分区：
文献类型：
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作者：
Zhiwu Lin;C. Zeng
我们考虑了由欧拉-泊松系统模拟的非旋转气态星的稳定性。在物态方程的一般假设下，我们证明了一个转折点原理（TPP），即恒星的稳定性完全取决于由中心密度参数化的质量-半径曲线。特别地，稳定性只能在极值处改变（即，局部最大值或最小值点）。对于一个非常一般的状态方程，TPP意味着随着中心密度的增加，恒星在第一个质量极大值之前是稳定的，而在超过这个点之后直到下一个质量极值（最小值）之前是不稳定的。此外，我们还得到了线性化Euler‐Poisson系统的不稳定模态的精确计数和指数截尾估计。为了证明这些结果，我们开发了一个一般框架的可分哈密顿偏微分方程。一般的方法是灵活的，可以用于许多其他问题，包括旋转和磁性恒星，相对论性恒星和星系的稳定性。© 2021 Wiley Periodicals LLC.
We consider stability of nonrotating gaseous stars modeled by the Euler‐Poisson system. Under general assumptions on the equation of states, we proved a turning point principle (TPP) that the stability of the stars is entirely determined by the mass–radius curve parametrized by the center density. In particular, the stability can only change at extrema (i.e., local maximum or minimum points) of the total mass. For a very general equations of state, TPP implies that for increasing center density the stars are stable up to the first mass maximum and unstable beyond this point until the next mass extremum (a minimum). Moreover, we get a precise counting of unstable modes and exponential trichotomy estimates for the linearized Euler‐Poisson system. To prove these results, we develop a general framework of separable Hamiltonian PDEs. The general approach is flexible and can be used for many other problems, including stability of rotating and magnetic stars, relativistic stars, and galaxies. © 2021 Wiley Periodicals LLC.