New method for blowup of the Euler-Poisson system

In this paper, we provide a new method for establishing the blowup of C-2 solutions for the pressureless Euler-Poisson system with attractive forces for R-N (N >= 2) with rho(0, x(0)) > 0 and Omega(0ij)(x(0)) = 1/2[partial derivative(j)(iu)(0, x(0)) - partial derivative(i)(ju) (0, x(0))] = 0 at some point x(0) is an element of R-N. By applying the generalized Hubble transformation div u(t, x(0)(t)) = N(a) over dot(t)/a(t) to a reduced Riccati differential inequality derived from the system, we simplify the inequality into the Emden equation (sic)(t) = lambda/a(t)(N-1), (a)(0) = 1, (a) over dot(0) = div u(0, x(0))/N. Known results on its blowup set allow us to easily obtain the blowup conditions of the Euler-Poisson system. Published by AIP Publishing.