论文标题
旋转气体的稳定性
Stability of rotating gaseous stars
论文作者
论文摘要
我们考虑通过具有一般状态方程的Euler-Poisson系统建模的旋转气体恒星的稳定性。当恒星的角速度是雷利稳定的时，我们证明了公理对称扰动的急剧稳定性标准。我们还获得了线性化的Euler-Poisson系统的不稳定模式和指数三分法的估计值。通过使用此稳定性标准，我们证明，对于由具有固定角速度曲线的中心密度参数化的缓慢旋转星的家族，转弯点原理是不正确的。也就是说，与非旋转恒星的情况不同，旋转恒星的稳定性变化不会发生在总质量的极端点。相比之下，我们证明了转弯点原理对于具有固定角动量分布的缓慢旋转恒星的家族是正确的。当角速度不稳定时，我们证明了旋转恒星的线性不稳定性。此外，我们对线性化的Euler-Poisson方程的光谱和急剧生长估计进行了完整描述。
We consider stability of rotating gaseous stars modeled by the Euler-Poisson system with general equation of states. When the angular velocity of the star is Rayleigh stable, we proved a sharp stability criterion for axi-symmetric perturbations. We also obtained estimates for the number of unstable modes and exponential trichotomy for the linearized Euler-Poisson system. By using this stability criterion, we proved that for a family of slowly rotating stars parameterized by the center density with fixed angular velocity profile, the turning point principle is not true. That is, unlike the case of non-rotating stars, the change of stability of the rotating stars does not occur at extrema points of the total mass. By contrast, we proved that the turning point principle is true for the family of slowly rotating stars with fixed angular momentum distribution. When the angular velocity is Rayleigh unstable, we proved linear instability of rotating stars. Moreover, we gave a complete description of the spectra and sharp growth estimates for the linearized Euler-Poisson equation.
