关于微分旋转恒星扰动与稳定性的框架

本文提供了一种关于线性各向同性拉格朗日扰动和微分旋转牛顿恒星稳定性的新框架。为此，我们克服了Dyson和Schutz之前框架中的问题，为对此类恒星稳定性的严密分析提供了基础。为此，振荡方程被写成时间上的一阶系统。从该系统中提取时间演化的生成器，并给出其生成强连续群的希尔伯特空间。因此，可靠地 initialValueProblem has a well-posed initial value problem. The spectrum of the generator relevant for stability considerations is shown to be equal to the spectrum of an operator polynomial whose coefficients can be read off from the governing equation. Finally, we give for the first time sufficient criteria for stability in the form of inequalities for the coefficients of the polynomial. These show that a negative canonical energy of the star does not necessarily indicate instability. It is still unclear whether these criteria are strong enough to prove stability for realistic stars.