Abstract
In the supercritical range of the polytropic indices γ∈(1,43) 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.
| Original language | English |
|---|---|
| Pages (from-to) | 957-1066 |
| Number of pages | 110 |
| Journal | Archive for Rational Mechanics and Analysis |
| Volume | 246 |
| Issue number | 2-3 |
| DOIs | |
| Publication status | Published - 16 Nov 2022 |
Bibliographical note
Acknowledgements: Y. Guo’s research is supported in part by NSF DMS-Grant 2106650. M. Hadži ´c’s and M. Schrecker’s research is supported by the EPSRC Early Career Fellowship EP/S02218X/1. J. Jang’s research is supported by the NSF DMS-Grant 2009458 and the Simons Fellowship (Grant Number 616364).Data Availability Statement: Data sharing not applicable to this article as no
datasets were generated or analysed during the current study