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Global regularity criterion for the Navier‐Stokes equations based on the direction of vorticity
Author(s) -
Zhang Zujin,
Wang Weihua,
Zhou Yong
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5818
Subject(s) - mathematics , vorticity , extension (predicate logic) , navier–stokes equations , mathematical analysis , vortex , compressibility , physics , meteorology , mechanics , computer science , programming language
We study the regularity criterion for the Navier‐Stokes equations and show that the ( β 1 , β 2 , β 3 )‐Hölder continuity assumption in ( x 1 , x 2 , x 3 ) on the direction of the vorticity ensures the regularity of the solution. This may be viewed as an extension of many previous results, since some of the β i can be arbitrarily small.
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