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arXiv · 1403.6234

Blowup for $C^{2}$ Solutions of the N-dimensional Euler-Poisson Equations in Newtonian Cosmology

Manwai Yuen
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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 $C^{2}$ solutions with a bounded domain, $\left\Vert X(t)\right\Vert \leq X_{0}$, where $\left\Vert\cdot\right\Vert $ denotes the volume and $X_{0}$ is a positive constant. In particular, we show that if the cosmological constant $Λ<M/X_{0}$, with the total mass $M$, then the non-trivial $C^{2}$ solutions in $R^{N}$ with the irrotational initial condition blow up at a finite time.

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Manwai Yuen. 2014-03-25. Blowup for $C^{2}$ Solutions of the N-dimensional Euler-Poisson Equations in Newtonian Cosmology. https://doi.org/10.1016/j.jmaa.2014.02.004

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