论文标题
可分离的汉密尔顿PDES和气态稳定性的转折点原理
Separable Hamiltonian PDEs and Turning point principle for stability of gaseous stars
论文作者
论文摘要
我们认为由Euler-Poisson系统建模的非旋转气体恒星的稳定性。在对状态方程式的一般假设下，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参数的质量 - 拉迪曲线确定。特别是，稳定性只能在总质量的超值（即局部最大值或最小点）上发生变化。对于非常通用的状态方程，TPP意味着，为了增加中心密度，恒星稳定至第一个质量最大和不稳定，直到下一个质量极值（最小值）。此外，我们获得了线性化的Euler-Poisson系统的不稳定模式和指数三分法估计的精确计数。为了证明这些结果，我们开发了可分离的哈密顿PDE的一般框架。一般方法是灵活的，可用于许多其他问题，包括旋转和磁星的稳定性，相对论恒星和星系。
We consider stability of non-rotating 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 parameterized 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 very general equation of states, TPP implies that for increasing center density the stars are stable up to the first mass maximum and unstable beyond this point until 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.
