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A sufficient condition for a finitetime $L_2 $ singularity of the 3d Euler Equations
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He, Xinyu. (2005) A sufficient condition for a finitetime $L_2 $ singularity of the 3d Euler Equations. Mathematical Proceedings of the Cambridge Philosophical Society, Vol.139 (No.3). pp. 555561. ISSN 03050041

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Official URL: http://dx.doi.org/10.1017/S0305004105008777
Abstract
A sufficient condition is derived for a finitetime $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 blowup time in $L_2 $.
Item Type:  Journal Article 

Subjects:  Q Science > QA Mathematics 
Divisions:  Faculty of Science > Mathematics 
Library of Congress Subject Headings (LCSH):  Fluid dynamics  Mathematical models, Fluid mechanics, Eigenvectors 
Journal or Publication Title:  Mathematical Proceedings of the Cambridge Philosophical Society 
Publisher:  Cambridge University Press 
ISSN:  03050041 
Official Date:  November 2005 
Volume:  Vol.139 
Number:  No.3 
Page Range:  pp. 555561 
Identification Number:  10.1017/S0305004105008777 
Status:  Peer Reviewed 
Access rights to Published version:  Open Access 
References:  [1] J. T. Beale, T. Kato and A. J. Majda. Remarks on the breakdown of smooth solutions for the 3d Euler equations. Comm. Math. Phys. 94 (1984), 61–66. 
URI:  http://wrap.warwick.ac.uk/id/eprint/737 
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