Larson-Penston Self-similar Gravitational Collapse

Abstract

Using numerical integration, in 1969 Penston [22] and Larson [17] independently discovered a self-similar solution describing the collapse of a self-gravitating asymptotically flat fluid with the isothermal equation of state $p=k\varrho$, $k>0$, and subject to Newtonian gravity. We rigorously prove the existence of such a Larson-Penston solution.

44 pages

References in corpus (8)

• Critical phenomena in gravitational collapse
• Global Smooth Ion Dynamics in the Euler-Poisson System
• Regularity of Solutions to Regular Shock Reflection for Potential Flow
• On smooth self similar solutions to the compressible Euler equations
• On the implosion of a three dimensional compressible fluid
• Critical phenomena in Newtonian gravity
• Multi-d Isothermal Euler Flow: Existence of unbounded radial similarity solutions
• Non-neutral global solutions for the electron Euler-Poisson system in 3D

Cited by in corpus (4)

• Gravitational Collapse for Polytropic Gaseous Stars: Self-similar Solutions
• Self-Similar Solutions to the Compressible Euler Equations and their Instabilities
• Smooth imploding solutions for 3D compressible fluids
• Global Finite-Energy Solutions of the Compressible Euler-Poisson Equations for General Pressure Laws with Spherical Symmetry