Perturbation Analysis of Gravitational Collapse of Gaseous Stars in the Pressureless Euler-Poisson System
Abstract
The compressible Euler-Poisson system describes the full evolutionary processes of inviscid compressible gases, including compression, expansion, fluid motion, equilibrium states and gravitational collapse, under the combined effects of self-gravitation, pressure and inertial forces. It constitutes the fundamental macroscopic mathematical model for describing stellar structures, nebular evolution and gravitational collapse of gaseous celestial bodies. The system comprises mass conservation, momentum conservation, energy conservation laws coupled with the Poisson equation. Following the research in \cite{huang2022}, this paper investigates the quantitative relations among the relative perturbation amplitude of initial velocity, critical time and collapse time for gaseous stars undergoing gravitational collapse within the framework of the pressureless Euler-Poisson system. The closed-form formulas are verified against direct numerical integration, the accuracy of the asymptotic power law is quantified, and the relation between the two time scales is examined.
Related
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- Global existence and time decay for a bipolar Euler-Poisson system with one pressureless and undamped fluid
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- Linear and Nonlinear Phase Mixing for the Gravitational Vlasov–Poisson System Under an External Kepler Potential
- Compact Core--Shell Equilibria in Gravitational Vlasov--Poisson Systems with Positive and Negative Mass
BibTeX
@misc{wang2026perturbation,
title = {{Perturbation Analysis of Gravitational Collapse of Gaseous Stars in the Pressureless Euler-Poisson System}},
author = {Xingchen Wang and Xiaomin Zhang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03061},
eprint = {2611.03061},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03061},
}
RIS
TY - UNPB
TI - Perturbation Analysis of Gravitational Collapse of Gaseous Stars in the Pressureless Euler-Poisson System
AU - Xingchen Wang
AU - Xiaomin Zhang
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03061
UR - https://arxiv.org/abs/2611.03061
AB - The compressible Euler-Poisson system describes the full evolutionary processes of inviscid compressible gases, including compression, expansion, fluid motion, equilibrium states and gravitational collapse, under the combined effects of self-gravitation, pressure and inertial forces. It constitutes the fundamental macroscopic mathematical model for describing stellar structures, nebular evolution and gravitational collapse of gaseous celestial bodies. The system comprises mass conservation, momentum conservation, energy conservation laws coupled with the Poisson equation. Following the research in \cite{huang2022}, this paper investigates the quantitative relations among the relative perturbation amplitude of initial velocity, critical time and collapse time for gaseous stars undergoing gravitational collapse within the framework of the pressureless Euler-Poisson system. The closed-form formulas are verified against direct numerical integration, the accuracy of the asymptotic power law is quantified, and the relation between the two time scales is examined.
ER -