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On the Finite-Time Blowup of a 1D Model for the 3D Incompressible Euler Equations

Hou, Thomas Y. and Luo, Guo (2013) On the Finite-Time Blowup of a 1D Model for the 3D Incompressible Euler Equations. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20160315-134409579

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Abstract

We study a 1D model for the 3D incompressible Euler equations in axisymmetric geometries, which can be viewed as a local approximation to the Euler equations near the solid boundary of a cylindrical domain. We prove the local well-posedness of the model in spaces of zero-mean functions, and study the potential formation of a finite-time singularity under certain convexity conditions for the velocity field. It is hoped that the results obtained on the 1D model will be useful in the analysis of the full 3D problem, whose loss of regularity in finite time has been observed in a recent numerical study (Luo and Hou, 2013).


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1311.2613arXivDiscussion Paper
Additional Information:Submitted on 13 Nov 2013. This work was supported in part by NSF FRG Grant DMS-1159138.
Funders:
Funding AgencyGrant Number
NSFDMS-1159138
Record Number:CaltechAUTHORS:20160315-134409579
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20160315-134409579
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:65369
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:15 Mar 2016 22:57
Last Modified:15 Mar 2016 22:57

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