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The classical model of an isolated selfgravitating gaseous star is given by the Euler–Poisson system with a polytropic pressure law P(ρ)=ργ, γ>1. For any 1<γ<43, we construct an infinite-dimensional family of collapsing solutions to the Euler–Poisson system whose density is in general space inhomogeneous and undergoes gravitational blowup along a prescribed space-time surface, with continuous mass absorption at the origin. The leading order singular behavior is described by an explicit collapsing solution of the pressureless Euler–Poisson system.
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An analysis of a 2 × 2 Keyfitz–Kranzer type balance system with varying generalized Chaplygin gas
We consider a system of two balance laws of Keyfitz–Kranzer type with varying generalized Chaplygin gas, which exhibits negative pressure and is a product of a function of time and the inverse of a power of the density. The Chaplygin gas is a fluid designed to accommodate measurements for the early universe and late-time universal expansion while obeying the pressure–density–time relation. We produce an explanation and description of the non-self-similar Riemann solutions, including the non-classical singular solutions. We also find that due to a direct dependence on time, a change in the regions allowing for combinations of classical and non-classical singular solutions occurs; therefore, a Riemann solution can have different solutions over several time intervals. Our findings are confirmed numerically using the Local Lax–Friedrichs scheme.
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- Award ID(s):
- 2349040
- PAR ID:
- 10572100
- Publisher / Repository:
- AIP Publishing
- Date Published:
- Journal Name:
- Physics of Fluids
- Volume:
- 36
- Issue:
- 9
- ISSN:
- 1070-6631
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1063/5.0231413
