Formation of singularities to the Euler–Poisson Equations

In this paper, the finite time blow-up of smooth solutions to the Cauchy problem for multi-dimensional Euler–Poisson equations is proved for a large class of initial data, which contains the cases of full Euler–Poisson equations and isentropic Euler–Poisson equations with repulsive forces or attractive. It does not require that the initial data have compact support or contain vacuum in any finite region.