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

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