恒星动力学：坍缩与膨胀

被真空包围的球对称各向同性弹性体的膨胀与坍缩

Expansion and collapse of spherically symmetric isotropic elastic bodies surrounded by vacuum

针对被真空包围、仅受内应力的球对称各向同性弹性体，本文构造尺度不变应变能函数，证明其可依残余压力符号发生无限膨胀或有限时间坍缩。

Continued Gravitational Collapse for Newtonian Stars

The classical model of an isolated selfrgavitating gaseous star is given by the Euler-Poisson system with a polytropic pressure law $P(ρ)=ρ^γ$, $γ>1$. For any $1<γ<\frac43$, we construct an infinite-dimensional family of collapsing solutions to the Euler-Poisson system whose density is in general space inhomogeneous and undergoes gravitational blowup along a prescribed space-time surface, with continuous mass absorption at the origin. The leading order singular behavior is described by an explicit collapsing solution of the pressureless Euler-Poisson system.

Gravitational Collapse for Polytropic Gaseous Stars: Self-similar Solutions

In the supercritical range of the polytropic indices $γ\in(1,\frac43)$ we show the existence of smooth radially symmetric self-similar solutions to the gravitational Euler-Poisson system. These solutions exhibit gravitational collapse in the sense that the density blows-up in finite time. Some of these solutions were numerically found by Yahil in 1983 and they can be thought of as polytropic analogues of the Larson-Penston collapsing solutions in the isothermal case $γ=1$. They each contain a sonic point, which leads to numerous mathematical difficulties in the existence proof.