Communications in Mathematical Sciences

Volume 6 (2008)

Number 3

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

Pages: 785 – 789

(Fast Communication)



Donghao Chae

Eitan Tadmor


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.


Euler-Poisson equations, finite time blow-up

2010 Mathematics Subject Classification

35B30, 35Q35

Published 1 January 2008