Nonradial stability of self-similarly expanding Goldreich-Weber stars
数学专题报告
报告题目(Title)：Nonradial stability of self-similarly expanding Goldreich-Weber stars
报告人(Speaker)：King Ming Lam（Delft University of Technology）
地点(Place)：Zoom ID: 89225968548, Password: 608098
时间(Time)：2025年10月27日（周一）17:00-18:00
邀请人(Inviter)：袁迪凡
报告摘要
A fundamental model of a self-gravitating star is given by the Euler-Poisson equation in the setting of a free boundary problem. At the mass critical index, there exists a class of spherically symmetric (self-similarly) expanding solutions, called the Goldreich-Weber solutions, modelling expanding stars. We establish non-radial non-linear stability of this class of solutions, extending existing results on radial stability. This in particular means we have proven global-in-time existence for a larger class of expanding solutions around the known class that’s not spherically symmetric but behaves similarly. To prove this result, we first proved a quantitative lower bound for the linearised operator against non-radial perturbations satisfying the natural orthogonality conditions, and then using it and the expansion-induced-dispersion to establish non-linear stability.
More precisely, any given self-similarly expanding Goldreich-Weber star is proved to be codimension-4 stable in the class of irrotational perturbations. The codimension-4 condition is optimal and reflects the presence of 4 unstable directions of the linearised operator in self-similar coordinates, which are induced by the conservation of the energy and the momentum. This result can be viewed as the codimension-1 nonlinear stability of the moduli space of self-similarly expanding GW-stars against irrotational perturbations.
主讲人简介
King Ming Lam did his PhD in UCL in London under Mahir Hadžić where he worked on the analysis of the Euler-Poisson equation modelling self gravitating stars; currently he is a postdoctoral researcher in Delft University of Technology in the group of Manuel Gnann researching contact line dynamics for free boundary flows.
