Blowup for C2C2 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 C2C2 solutions with a bounded domain, ‖X(t)‖⩽X0‖X(t)‖⩽X0, where ‖⋅‖‖⋅‖ denotes the volume and X0X0 is a positive constant. In particular, we show that if the cosmological constant Λ