报告时间：2022/11/15(周二) 15:00-17:00

报告地点：腾讯会议号：423-721-171

报告题目：Continued gravitational collapse for gaseous star and pressureless Euler-Poisson system

报告摘要：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.

报告人简介： 黄飞敏，中科院华罗庚首席研究员。主要从事非线性偏微分方程的研究工作，在非线性双曲守恒律、可压缩Navier-Stokes方程、Boltzmann方程等重要领域取得一系列突出成果，广受国内外同行的关注。解决了等温气体动力学方程组（即绝热指数\gamma=1）带真空的Cauchy问题弱解的整体存在性这一长期未解决的数学难题。在Hilbert第六问中取得突破性的进展，在Riemann解情形下验证Boltzmann方程到可压缩Euler方程的流体动力学极限。在组合波的稳定性的理论研究中，取得了一系列突破性进展，证明了基本波的若干组合的稳定性。曾获2013年国家自然科学奖二等奖（排名第一，第一完成人），国家杰出青年基金获得者，获2004年美国工业与应用数学协会杰出论文奖。