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

被引:17
|
作者
Grujic, Zoran [1 ]
Guberovic, Rafaela [1 ,2 ]
机构
[1] Univ Virginia, Dept Math, Charlottesville, VA 22904 USA
[2] Seminar Angew Math, CH-8092 Zurich, Switzerland
关键词
NAVIER-STOKES EQUATIONS; SUITABLE WEAK SOLUTIONS; INTERIOR REGULARITY; PLURISUBHARMONIC MEASURES; SPACES;
D O I
10.1007/s00220-010-1000-4
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
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 R-3 x (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-infinity-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.
引用
收藏
页码:407 / 418
页数:12
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