Continued Gravitational Collapse for Newtonian Stars

Abstract

AbstractThe 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 > 1 . For any $$1<\gamma <\frac{4}{3}$$ 1 < γ < 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.