On the Regularity Conditions of Suitable Weak Solutions of the 3D Navier–Stokes Equations

. Let v and ω be the velocity and the vorticity of the a suitable weak solution of the 3D Navier–Stokes equations in a space-time domain containing , and let be a parabolic cylinder in the domain. We show that if either with with , where L γ, α x , t denotes the Serrin type of class, then z 0 is a r...

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Bibliographic Details
Published inJournal of mathematical fluid mechanics Vol. 12; no. 2; pp. 171 - 180
Main Author Chae, Dongho
Format Journal Article
LanguageEnglish
Published Basel Birkhäuser-Verlag 01.05.2010
Subjects
Classical and Continuum Physics
Fluid- and Aerodynamics
Mathematical Methods in Physics
Physics
Physics and Astronomy
76D03
Navier–Stokes equations
weak solutions
76D05
35Q30
regularity criterion
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Summary:. Let v and ω be the velocity and the vorticity of the a suitable weak solution of the 3D Navier–Stokes equations in a space-time domain containing , and let be a parabolic cylinder in the domain. We show that if either with with , where L γ, α x , t denotes the Serrin type of class, then z 0 is a regular point for ν . This refines previous local regularity criteria for the suitable weak solutions.
ISSN:1422-6928
1422-6952
DOI:10.1007/s00021-008-0280-3