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A sufficient condition for a finite-time $L_2 $ singularity of the 3d Euler Equations
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He, Xinyu (2005) A sufficient condition for a finite-time $L_2 $ singularity of the 3d Euler Equations. Mathematical Proceedings of the Cambridge Philosophical Society, Vol.139 (No.3). pp. 555-561. doi:10.1017/S0305004105008777 ISSN 0305-0041.
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Official URL: http://dx.doi.org/10.1017/S0305004105008777
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 $.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > 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: | 0305-0041 | ||||
Official Date: | November 2005 | ||||
Dates: |
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Volume: | Vol.139 | ||||
Number: | No.3 | ||||
Page Range: | pp. 555-561 | ||||
DOI: | 10.1017/S0305004105008777 | ||||
Status: | Peer Reviewed | ||||
Access rights to Published version: | Open Access (Creative Commons) |
Data sourced from Thomson Reuters' Web of Knowledge
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