Space-time localization of a class of geometric criteria for preventing blow-up in the 3D NSE

A class of local (in the space-time) conditions on the vorticity directions implying local regularity of weak solutions to the 3D Navier-Stokes equations is established. In all the preceding results, the relevant geometric conditions, although being local in nature, have been assumed uniformly throu...

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Bibliographic Details
Published in:Communications in mathematical physics 2006-03, Vol.262 (3), p.555-564
Main Authors: GRUJIE, Zoran, ZHANG, Qi S
Format: Article
Language:English
Subjects:
Computational methods in fluid dynamics
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Mathematical analysis
Mathematics
Partial differential equations
Physics
Sciences and techniques of general use
Spacetime
Vorticity
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Summary:A class of local (in the space-time) conditions on the vorticity directions implying local regularity of weak solutions to the 3D Navier-Stokes equations is established. In all the preceding results, the relevant geometric conditions, although being local in nature, have been assumed uniformly throughout the spatial regions of high vorticity magnitude, and uniformly in time. In addition, similar results are obtained assuming a less restrictive integral condition on the vorticity directions.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-005-1437-z