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## A sufficient condition for a finite-time $L_2$ singularity of the 3d Euler Equations

### Abstract

A sufficient condition is derived for a finite-time $L_2$ singularity of the 3d incompressible Euler equations, making appropriate assumptions on eigenvalues of the Hessian of pressure. Under this condition $\ \lim_{ t \uparrow T_*} \sup \|\frac{ D \omega} { Dt}\|_{L_2(\Omega)} = \infty$, where $\Omega \subset \mathbb{R}$ moves with the fluid. In particular, $| \omega |$, $| \S_{ij} |$, and $| \P_{ij} |$ all become unbounded at one point $(x_1, T_1)$, $T_1$ being the first blow-up time in $L_2$

Topics: QA
Publisher: Cambridge University Press
Year: 2005
OAI identifier: oai:wrap.warwick.ac.uk:737

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