论文标题
扩展Goldreich-Weber星星的非自由稳定性
Nonradial stability of expanding Goldreich-Weber stars
论文作者
论文摘要
Goldreich-Weber解决方案构成了扩展和崩溃的解决方案的有限参数。该家族的两个子类对应于由恒星的动态半径适当调节的紧凑型密度曲线，以自相似的速率$λ（t）_ {t \ to \ infty} \ sim t^{\ sim t^{\ frac23} $和线性费率$ $ c $λ（t）我们证明了两个结果：任何线性扩展的Goldreich-Weber恒星都是非线性稳定的，而任何给定的自我相似扩展的Goldreich-Weber Star都是Codimension-4非线性稳定，以防止扰动。 后一个结果中的Codimension-4条件是最佳的，并且反映了自相似坐标中线性化动力学中4个不稳定方向的存在，这些方向是由能量和动量的保护引起的。该结果可以看作是模量空间的codimension-1非线性稳定性，这是自相似的戈德里希·韦伯恒星，反对无关扰动。
Goldreich-Weber solutions constitute a finite-parameter of expanding and collapsing solutions to the mass-critical Euler-Poisson system. Two subclasses of this family correspond to compactly supported density profiles suitably modulated by the dynamic radius of the star that expands at the self-similar rate $λ(t)_{t\to\infty}\sim t^{\frac23}$ and linear rate $λ(t)_{t\to\infty}\sim t$ respectively. We prove two results: any linearly expanding Goldreich-Weber star is nonlinearly stable, while any given self-similarly expanding Goldreich-Weber star is codimension-4 nonlinearly stable against irrotational perturbations. The codimension-4 condition in the latter result is optimal and reflects the presence of 4 unstable directions in the linearised dynamics in self-similar coordinates, which are induced by the conservation of the energy and the momentum. This result can be viewed as a codimension-1 nonlinear stability of the moduli space of self-similarly expanding Goldreich-Weber stars against irrotational perturbations.
