Continued Gravitational Collapse for Newtonian Stars

Guo, Yan; Hadžić, Mahir; Jang, Juhi

doi:10.1007/s00205-020-01580-w

Cited by 24 publications

(19 citation statements)

References 54 publications

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“…The solutions constructed in Theorem 1.3 (1 < γ < 4 3 ) are very different from the GW solutions (γ = 4 3 ), and owe their existence to a subtle balancing of the three dominant forces in the problem: inertia, pressure, and gravity. A completely different portion of the phase-space is populated by the so-called dust-like collapsing stars, which have been shown to exist in [12]. The solutions constructed in [12] do not honour the scaling invariance implied by (1.5), but are instead to a leading order approximated by the so-called dust solutions, which solve (1.1)-(1.2) without the pressure term p.…”

Section: Introduction and The Main Resultsmentioning

confidence: 99%

“…A completely different portion of the phase-space is populated by the so-called dust-like collapsing stars, which have been shown to exist in [12]. The solutions constructed in [12] do not honour the scaling invariance implied by (1.5), but are instead to a leading order approximated by the so-called dust solutions, which solve (1.1)-(1.2) without the pressure term p.…”

Section: Introduction and The Main Resultsmentioning

confidence: 99%

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Gravitational Collapse for Polytropic Gaseous Stars: Self-similar Solutions

Guo

Hadžić²,

Jang³

et al. 2021

Preprint

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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.

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Section: Introduction and The Main Resultsmentioning

confidence: 99%

Section: Introduction and The Main Resultsmentioning

confidence: 99%

Gravitational Collapse for Polytropic Gaseous Stars: Self-similar Solutions

Guo

Hadžić²,

Jang³

et al. 2021

Preprint

Self Cite

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show abstract

“…The nonlinear stability in the expanding case was shown in [13]. When 1 < γ < 4 3 the authors in [9] showed the existence of an infinite-dimensional class of collapsing solutions to the gravitational Euler-Poisson system. When one considers the Euler-Poisson system with an electric (instead of gravitational) force field, the dispersive nature of the problem becomes dominant.…”

Section: Isothermal Euler-poisson Systemmentioning

confidence: 99%

Larson–Penston Self-similar Gravitational Collapse

Guo

Hadžić

Jang

2021

Commun. Math. Phys.

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Using numerical integration, in 1969 Penston (Mon Not R Astr Soc 144:425–448, 1969) and Larson (Mon Not R Astr Soc 145:271–295, 1969) independently discovered a self-similar solution describing the collapse of a self-gravitating asymptotically flat fluid with the isothermal equation of state $$p=k\varrho $$ p = k ϱ , $$k>0$$ k > 0 , and subject to Newtonian gravity. We rigorously prove the existence of such a Larson–Penston solution.

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“…When the initial density is small and has compact support, Hadzic-Jang [31] constructed a class of global-in-time solutions of the 3-D CEPEs in the Lagrangian coordinates for γ = 1 + 1 k , k ∈ N\{1} or γ ∈ (1, 14 13 ). More recently, Guo-Hadzic-Jang [26] constructed an infinite-dimensional family of collapsing solutions of CEPEs (1.1). We also refer [44,54,56] for the local well-posedness of smooth solutions.…”

Section: Introductionmentioning

confidence: 99%

Global Solutions of the Compressible Euler-Poisson Equations with Large Initial Data of Spherical Symmetry

Chen,

He,

Wang

et al. 2021

Preprint

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We are concerned with a global existence theory for finite-energy solutions of the multidimensional Euler-Poisson equations for both compressible gaseous stars and plasmas with large initial data of spherical symmetry. One of the main challenges is the strengthening of waves as they move radially inward towards the origin, especially under the self-consistent gravitational field for gaseous stars. A fundamental unsolved problem is whether the density of the global solution forms concentration to become a delta measure at the origin. To solve this problem, we develop a new approach for the construction of approximate solutions as the solutions of an appropriately formulated free boundary problem for the compressible Navier-Stokes-Poisson equations with a carefully adapted class of degenerate density-dependent viscosity terms, so that a rigorous convergence proof of the approximate solutions to the corresponding global solution of the compressible Euler-Poisson equations with large initial data of spherical symmetry can be obtained. Even though the density may blow up near the origin at certain time, it is proved that no concentration (delta measure) is formed in the vanishing viscosity limit for the finite-energy solutions of the compressible Euler-Poisson equations for both gaseous stars and plasmas in the physical regimes under consideration.

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Continued Gravitational Collapse for Newtonian Stars

Abstract: The classical model of an isolated selfgravitating gaseous star is given by the Euler–Poisson system with a polytropic pressure law $$P(\rho )=\rho ^\gamma $$ P ( ρ ) = ρ γ , $$\gamma >1$$ γ > … Show more

Cited by 24 publications

References 54 publications

Gravitational Collapse for Polytropic Gaseous Stars: Self-similar Solutions

Gravitational Collapse for Polytropic Gaseous Stars: Self-similar Solutions

Larson–Penston Self-similar Gravitational Collapse

Global Solutions of the Compressible Euler-Poisson Equations with Large Initial Data of Spherical Symmetry

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