学术报告（黄飞敏 11.16）

The gravitational collapse of an isolated self-gravitating gaseous star for $\gamma$-law pressure $p(\rho)=\rho^\gamma$ ($1<\gamma<\frac43$) in the mass-supcritical case is investigated. In this talk, all spherically symmetric solutions of the pressureless Euler-Poisson system are classified. Precisely speaking, for fixed radius $r$, there exists a unique critical velocity $v^*(r)>0$ depending on the mean density in the ball $B(0,r)$ for the pressureless Euler-Poisson system such that if the initial
velocity $\chi_1(r)\geq v^*(r)$ (Escape case), then the dust runs away from the gravitational force forever along an escape trajectory, and if the initial velocity $\chi_1(r)< v^*(r)$ (Collapse case), then the dust collapses at the origin in a finite time $t^*(r)$ even it expands initially, i.e., $\chi_1(r)>0$. Moreover, it is proved that there exist a class of spherically symmetric solutions of gaseous star, which formulate a continued gravitational collapse in finite time, based on the background of the pressureless solutions if $\chi_1(r)< v^*(r)$ for all $r\in[0,1]$. It is noted that $\chi_1(r)$ could be positive, that is, the star might expand
initially, but finally collapse. The talk is based on a joint work with Yue Yao.