Long-time behaviours of classical solutions to relativistic Euler-Poisson equations

In this paper, long-time behaviours of classical solutions to relativistic Euler-Poisson equations in radial symmetry (REPE) are investigated. First, we establish the finite propagation speed property of the REPE system and the propagation speed sigma is found to be sigma := root 8 pi M/R(1 + e/c(2)) + c(2), where all constants are given parameters or initial data to the system. Subsequently, we show that if the initial functional integral(R)(0) v(0, r)dr is sufficiently large, then the classical solutions of the REPE will blow up on finite time, where v(0, r) is the initial velocity component of REPE and R is the radius of support of the initial mass-energy density.