The anisotropic regularity criteria for 3D Navier–Stokes equations involving one velocity component

The anisotropic regularity criterion for the Navier–Stokes equations in terms of the one component of the velocity gradient (∂iuj,1≤i,j≤3) is investigated. It is an improvement of results of Qian (2016) and is also a complement of the results of Guo et al. (2018) for i=j. Besides, the consistent reg...

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Published in:Nonlinear analysis: real world applications 2020-08, Vol.54, p.103094, Article 103094
Main Author: Qian, Chenyin
Format: Article
Language:English
Subjects:
Anisotropic regularity criterion
Computational fluid dynamics
Criteria
Fluid flow
Leray–Hopf weak solution
Mathematical analysis
Navier-Stokes equations
Regularity
Velocity distribution
Velocity gradient
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description The anisotropic regularity criterion for the Navier–Stokes equations in terms of the one component of the velocity gradient (∂iuj,1≤i,j≤3) is investigated. It is an improvement of results of Qian (2016) and is also a complement of the results of Guo et al. (2018) for i=j. Besides, the consistent regularity criterion without distinguishing i=j and i≠j is also obtained. Finally, the regularity result based on the fractional derivatives for one component of the velocity field Dhαu3 with α∈[0,1] is also established, which can be reduced to some previous results with α=0 and α=1.
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subjects Anisotropic regularity criterion
Computational fluid dynamics
Criteria
Fluid flow
Leray–Hopf weak solution
Mathematical analysis
Navier-Stokes equations
Regularity
Velocity distribution
Velocity gradient
title The anisotropic regularity criteria for 3D Navier–Stokes equations involving one velocity component
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