Blowing up solutions of the euler-poisson equation for the evolution of gaseous stars

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Abstract
The adiabatic hydrodynamical evolution of a star regarded as an isentropic ideal gas with self-gravitation is governed by the Euler-Poisson equation. Although the initial value problem associated with this equation was solved for so-called tame initial data, the life span of any nontrivial tame solution is considered to be finite. Therefore one might expect that we could solve the equation in the frame-work of weak solutions globally in time. However, this paper shows that there exist blowing up solutions which tend to the delta function after finite times. This fact demonstrates the necessity of some restrictions on initial data for getting temporarily global solutions.

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