Paper Info
Title
CONTINUED GRAVITATIONAL COLLAPSE FOR GASEOUS STAR AND PRESSURELESS EULER-POISSON SYSTEM
Abstract
The gravitational collapse of an isolated self-gravitating gaseous star for gamma-law pressure p(rho) = rho(gamma) (1 < gamma < 4/3) in the mass-sup critical case is investigated. It was first shown in [Y. Guo, M. Hadzic and J. Jang, Arch. Rational Mech. Anal., 239 (2021), pp. 431-552]. that there exists a kind of continued gravitational collapse, and the collapse is based on a special solution of the pressureless Euler-Poisson system. In this paper, all spherically symmetric solutions of the pressureless Euler-Poisson system are classified. Precisely speaking, for fixed radius r, there exists a unique critical velocity v(*)(r) > 0 depending on the mean density in the ball B(0, r) for the pressureless Euler-Poisson system such that if the initial velocity chi 1(r) >= v*(r) (escape case), then the dust runs away from the gravitational force forever along an escape trajectory, and if the initial velocity chi 1(r) < v(*)(r) (collapse case), then the dust collapses at the origin in a finite time t(*)(r) even if it expands initially, i.e., chi 1(r) > 0. Moreover, it is proved that there exists a class of spherically symmetric solutions of a gaseous star, which formulates a continued gravitational collapse in finite time, based on the background of the pressureless solutions if chi 1(r) < v*(r) for all r is an element of [0, 1]. It is noted that chi 1(r) could be positive; that is, the star might expand initially but finally collapse.
Year
DOI
Venue
2022
10.1137/21M1450902
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Keywords
DocType
Volume
gravitational collapse, gaseous star, pressureless Euler-Poisson system
Journal
54
Issue
ISSN
Citations 
3
0036-1410
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Feimin Huang1117.68
Yue Yao200.34