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Separable Hamiltonian PDEs and Turning Point Principle for Stability of Gaseous Stars
Communications on Pure and Applied Mathematics ( IF 3 ) Pub Date : 2021-11-08 , DOI: 10.1002/cpa.22027
Zhiwu Lin 1 , Chongchun Zeng 1
Affiliation  

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.

中文翻译:

气态星稳定性的可分离哈密顿偏微分方程和转折点原理

我们考虑由欧拉-泊松系统模拟的非旋转气态星的稳定性。在状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由中心密度参数化的质量半径曲线决定。特别是,稳定性只能在总质量的极值点(即局部最大值或最小值点)发生变化。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,恒星在第一个质量最大值之前是稳定的,而超过这个点则不稳定,直到下一个质量极值(最小值)。此外,我们得到了线性欧拉-泊松系统的不稳定模态和指数三分法估计的精确计数。为了证明这些结果,我们开发了可分离哈密顿偏微分方程的一般框架。一般方法很灵活,可用于许多其他问题,包括旋转和磁星、相对论恒星和星系的稳定性。© 2021 威利期刊有限责任公司。
更新日期:2021-11-08
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