Blow-up of Smooth Solutions to the Euler-Poisson Equations

Abstract: In this paper, the finite time blow-up of smooth solutions to the Cauchy problem for full Euler-Poisson equations and isentropic Euler-Poisson equations with repulsive forces or attractive forces in high dimensions $(n\geq3)$ is proved for a large class of initial data. It is not required that the initial data has compact support or contains vacuum in any finite regions.