Continued collapse, linear expansion for gaseous star and pressureless Euler-Poisson system
数学专题报告
报告题目(Title)：Continued collapse, linear expansion for gaseous star and pressureless Euler-Poisson system
报告人(Speaker)：姚悦 博士 中科院数学与系统科学研究院
地点(Place)：118-979-163
时间(Time)：2022年 5 月31 日 （周二）16:30-17:30
邀请人(Inviter)：袁迪凡
报告摘要
It is well-known that the classical model of an isolated self-gravitating gaseous star is given by the Euler-Poisson system with gravitational effects. The well-posedness of this system has been an open problem in mathematics. In this talk, we firstly classify all spherically symmetric solutions of the pressureless Euler-Poisson system and observe that there exists a unique critical velocity such that if the initial velocity is larger than the critical speed, then the dust runs away from the gravitational force forever, and if the initial velocity is smaller than the critical speed, then the dust collapses at the origin in a finite time. Based on the observation, we constructed a class of continued collapse solutions and linear expansion solutions for gaseous star with $\gamma$-law pressure ($1<\gamma<\frac43$) respectively. The talk is based on the joint work with Prof. Feimin Huang (Chinese Academy of Sciences).
