Continued Gravitational Collapse for Newtonian Stars

Abstract

The classical model of an isolated selfrgavitating gaseous star is given by the Euler-Poisson system with a polytropic pressure law $P(\rho )={\rho }^{\gamma }$, $\gamma >1$. For any $1<\gamma <\frac{4}{3}$, 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.

103 pages, 2 figures