On the finite time blow-up of the Euler-Poisson equations in $\Bbb R^{2}$

We prove the finite time blow-up for $C^1$ solutions of the attractive Euler-Poisson equations in $\Bbb R^{2}$, $n\geq1$, with and without background state, for a large set of 'generic' initial data. We characterize this supercritical set by tracing the spectral dynamics of the deformation and vorticity tensors.

Keywords

Euler-Poisson equations, finite time blow-up

2010 Mathematics Subject Classification

35B30, 35Q35

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Published 1 January 2008