A Spatially Localized l log l Estimate on the Vorticity in the 3D NSE

The purpose of this note is to present a spatially localized l log l bound on the vorticity in the 3D Navier-Stokes equations, assuming a very mild, purely geometric condition. This yields an extra-log decay of the distribution function of the vorticity, which in turn implies breaking the criticalit...

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Bibliographic Details
Published in:Indiana University mathematics journal 2015-01, Vol.64 (2), p.433-440
Main Authors: Bradshaw, Zachary, Grujić, Zoran
Format: Article
Language:English
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Summary:The purpose of this note is to present a spatially localized l log l bound on the vorticity in the 3D Navier-Stokes equations, assuming a very mild, purely geometric condition. This yields an extra-log decay of the distribution function of the vorticity, which in turn implies breaking the criticality in a physically, numerically, and mathematical analysis-motivated criticality scenario based on vortex stretching and anisotropic diffusion.
ISSN:0022-2518
1943-5258
DOI:10.1512/iumj.2015.64.5496