Localization of Analytic Regularity Criteria on the Vorticity and Balance Between the Vorticity Magnitude and Coherence of the Vorticity Direction in the 3D NSE |
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Authors: | Zoran Gruji? Rafaela Guberovi? |
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Institution: | (1) Department of Mathematics, University of British Columbia, Vancouver, BC, Canada, V6T 1Z2;(2) Department of Mathematics, Sungkyunkwan University and Institute of Basic Science, Suwon, 440-746, Republic of Korea |
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Abstract: | 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
\mathbbR3 ×(0,T){\mathbb{R}^3 \times (0,T)} 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. |
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Keywords: | |
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