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arXiv · 2107.12056

Gravitational Collapse for Polytropic Gaseous Stars: Self-similar Solutions

Yan Guo·Mahir Hadzic·Juhi Jang·Matthew Schrecker
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Abstract

In the supercritical range of the polytropic indices $\gamma\in(1,\frac43)$ 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 $\gamma=1$. They each contain a sonic point, which leads to numerous mathematical difficulties in the existence proof.

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Yan Guo, Mahir Hadzic, Juhi Jang, Matthew Schrecker. 2021-07-26. Gravitational Collapse for Polytropic Gaseous Stars: Self-similar Solutions. https://doi.org/10.1007/s00205-022-01827-8

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