Gravitational Collapse for Polytropic Gaseous Stars: Self-Similar Solutions
Gravitational Collapse for Polytropic Gaseous Stars: Self-Similar Solutions
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DOI：
10.1007/s00205-022-01827-8
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发表时间：
2022-11-16
影响因子：
2.5
通讯作者：
Schrecker, Matthew
中科院分区：
文献类型：
--
作者：
Guo, Yan;Hadzic, Mahir;Schrecker, Matthew
在多方指数的超临界范围内，γ是（1，4/3）的元素，我们证明了引力Euler-Poisson系统的光滑径向对称自相似解的存在性.这些解在密度在有限时间内爆炸的意义上表现出引力坍缩。其中一些解是Yahil在1983年数值计算得到的，它们可以被认为是在γ = 1的等温情形下Larson-Penston坍缩解的多变类似物。它们每个都包含一个音速点，这导致了存在性证明中的许多数学困难。
In the supercritical range of the polytropic indices gamma is an element of (1, 4/3) 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 gamma = 1. They each contain a sonic point, which leads to numerous mathematical difficulties in the existence proof.