Localization of Analytic Regularity Criteria on the Vorticity and Balance Between the Vorticity Magnitude and Coherence of the Vorticity Direction in the 3D NSE

The first part of the paper provides spatio-temporal localization of a family of analytic regularity classes for the 3D NSE obtained by Beirao Da Veiga (space-time integrability of the gradient of the velocity on which is out of the range of the Sobolev embedding theorem reduction to the classical F...

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Bibliographic Details
Published inCommunications in mathematical physics Vol. 298; no. 2; pp. 407 - 418
Main Authors Grujić, Zoran, Guberović, Rafaela
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 01.09.2010
Subjects
Classical and Quantum Gravitation
Complex Systems
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
Parabolic Cylinder
Regularity Criterion
Vorticity
Vorticity Magnitude
Suitable Weak Solution
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Summary:The first part of the paper provides spatio-temporal localization of a family of analytic regularity classes for the 3D NSE obtained by Beirao Da Veiga (space-time integrability of the gradient of the velocity on which is out of the range of the Sobolev embedding theorem reduction to the classical Foias-Ladyzhenskaya-Prodi-Serrin space-time integrability conditions on the velocity) as well as the localization of the Beale-Kato-Majda regularity criterion (time integrability of the L ∞ -norm of the vorticity). The second part introduces a family of local, scaling invariant, hybrid geometric-analytic classes in which coherence of the vorticity direction serves as a weight in the local spatio-temporal integrability of the vorticity magnitude.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-010-1000-4