Blowup for C2 solutions of the N-dimensional Euler-Poisson equations in Newtonian cosmology

Pressureless Euler-Poisson equations with attractive forces are standard models in Newtonian cosmology. In this article, we further develop the spectral dynamics method and apply a novel spectral-dynamics-integration method to study the blowup conditions for C-2 solutions with a bounded domain, parallel to X(t)parallel to <= X-0, where parallel to.parallel to denotes the volume and X-0 is a positive constant. In particular, we show that if the cosmological constant A < M/X-0, with the total mass M, then the non-trivial C-2 solutions in R-N with the initial condition Omega(0ij) (x) = 1/2 [partial derivative(i)u(j) (0, x) - partial derivative(j)u(i) (0, x)] = 0 blow up at a finite time. (C) 2014 Elsevier Inc. All rights reserved.