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Improved Geometric Conditions for Non-Blowup of the 3D Incompressible Euler Equation

Deng, Jian and Hou, Thomas Y. and Yu, Xinwei (2006) Improved Geometric Conditions for Non-Blowup of the 3D Incompressible Euler Equation. Communications in Partial Differential Equations, 31 (2). pp. 293-306. ISSN 0360-5302. https://resolver.caltech.edu/CaltechAUTHORS:20170408-133541409

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Abstract

This is a follow-up of our recent article Deng et al. (2004 Deng, J.,Hou, T. Y., Yu, X. (2004). ). In Deng et al. (2004), we derive some local geometric conditions on vortex filaments which can prevent finite time blowup of the 3D incompressible Euler equation. In this article, we derive improved geometric conditions which can be applied to the scenario when velocity blows up at the same time as vorticity and the rate of blowup of velocity is proportional to the square root of vorticity. This scenario is in some sense the worst possible blow-up scenario for velocity field due to Kelvin's circulation theorem. The improved conditions can be checked by numerical computations. This provides a sharper local geometric constraint on the finite time blowup of the 3D incompressible Euler equation.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1080/03605300500358152DOIArticle
http://www.tandfonline.com/doi/abs/10.1080/03605300500358152PublisherArticle
Additional Information:© 2006 Taylor & Francis Group. Received October 1, 2004; Accepted August 1, 2005. This work was supported in part by NSF under the grant DMS-0073916 and ITR grant ACI-0204932.
Funders:
Funding AgencyGrant Number
NSFDMS-0073916
NSFACI-0204932
Subject Keywords:3D Euler equations, Finite time blowup, Geometric properties, Global existence
Issue or Number:2
Classification Code:Mathematics Subject Classification: Primary 76B03, Secondary 35L60, 35M10
Record Number:CaltechAUTHORS:20170408-133541409
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170408-133541409
Official Citation:Jian Deng , Thomas Y. Hou & Xinwei Yu (2006) Improved Geometric Conditions for Non-Blowup of the 3D Incompressible Euler Equation, Communications in Partial Differential Equations, 31:2, 293-306, DOI: 10.1080/03605300500358152
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:75864
Collection:CaltechAUTHORS
Deposited By: 1Science Import
Deposited On:13 Apr 2017 19:40
Last Modified:03 Oct 2019 16:55

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