Abstract
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 C2 solutions with a bounded domain, ‖X(t)‖⩽X0, where ‖⋅‖ denotes the volume and X0 is a positive constant. In particular, we show that if the cosmological constant Λ<M/X0, with the total mass M, then the non-trivial C2 solutions in RN with the initial condition Ω0ij(x)=12[∂iuj(0,x)−∂jui(0,x)]=0 blow up at a finite time.
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