The finite time blow-up for the Euler-Poisson equations in $\Bbb R^n$

Details The finite time blow-up for the Euler-Poisson equations in $\Bbb R^n$ The finite time blow-up for the Euler-Poisson equations in $\Bbb R^n$

2008-03-12

arxiv.org/abs/0803.1788v1

Mathematics

Analysis of PDEs

11 pages

Scientific paper

We prove the finite time blow-up for $C^1$ solutions to the Euler-Poisson
equations in $\Bbb R^n$, $n\geq 1$, with/without background density for initial
data satisfying suitable conditions. We also find a sufficient condition for
the initial data such that $C^3$ solution breaks down in finite time for the
compressible Euler equations for polytropic gas flows.

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