On the regularity criterion for the Navier–Stokes equations involving the diagonal entry of the velocity gradient

Nonlinear Analysis ◽

10.1016/j.na.2015.04.005 ◽

2015 ◽

Vol 122 ◽

pp. 169-175 ◽

Cited By ~ 1

Author(s):

Zujin Zhang ◽

Xian Yang

Keyword(s):

Velocity Gradient ◽

Stokes Equations ◽

Regularity Criterion ◽

Diagonal Entry ◽

Navier Stokes ◽

Navier Stokes Equations

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A regularity criterion for the Navier–Stokes equations via one diagonal entry of the velocity gradient

Communications in Mathematical Sciences ◽

10.4310/cms.2021.v19.n4.a10 ◽

2021 ◽

Vol 19 (4) ◽

pp. 1101-1112

Author(s):

Zdeněk Skalák

Keyword(s):

Velocity Gradient ◽

Stokes Equations ◽

Regularity Criterion ◽

Diagonal Entry ◽

Navier Stokes ◽

Navier Stokes Equations

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A refined regularity criterion for the Navier–Stokes equations involving one non-diagonal entry of the velocity gradient

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2017.04.049 ◽

2017 ◽

Vol 453 (2) ◽

pp. 1145-1150 ◽

Cited By ~ 8

Author(s):

Zujin Zhang ◽

Dingxing Zhong ◽

Xiantong Huang

Keyword(s):

Velocity Gradient ◽

Stokes Equations ◽

Regularity Criterion ◽

Diagonal Entry ◽

Navier Stokes ◽

Navier Stokes Equations

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The regularity criterion for 3D Navier–Stokes equations involving one velocity gradient component

Nonlinear Analysis ◽

10.1016/j.na.2012.09.019 ◽

2013 ◽

Vol 78 ◽

pp. 86-103 ◽

Cited By ~ 24

Author(s):

Daoyuan Fang ◽

Chenyin Qian

Keyword(s):

Velocity Gradient ◽

Stokes Equations ◽

Regularity Criterion ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Gradient Component

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A New Regularity Criterion for the 3D Navier-Stokes Equations via Two Entries of the Velocity Gradient Tensor

Acta Applicandae Mathematicae ◽

10.1007/s10440-013-9834-3 ◽

2013 ◽

Vol 129 (1) ◽

pp. 175-181 ◽

Cited By ~ 9

Author(s):

Zujin Zhang ◽

Dingxing Zhong ◽

Lin Hu

Keyword(s):

Velocity Gradient ◽

Stokes Equations ◽

Regularity Criterion ◽

Navier Stokes ◽

Gradient Tensor ◽

Navier Stokes Equations ◽

Velocity Gradient Tensor

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Global Regularity Criterion for the 3D Navier–Stokes Equations Involving One Entry of the Velocity Gradient Tensor

Archive for Rational Mechanics and Analysis ◽

10.1007/s00205-011-0439-6 ◽

2011 ◽

Vol 202 (3) ◽

pp. 919-932 ◽

Cited By ~ 112

Author(s):

Chongsheng Cao ◽

Edriss S. Titi

Keyword(s):

Velocity Gradient ◽

Global Regularity ◽

Stokes Equations ◽

Regularity Criterion ◽

Navier Stokes ◽

Gradient Tensor ◽

Navier Stokes Equations ◽

Velocity Gradient Tensor

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A new local regularity criterion for suitable weak solutions of the Navier–Stokes equations in terms of the velocity gradient

Mathematische Annalen ◽

10.1007/s00208-017-1522-6 ◽

2017 ◽

Vol 370 (1-2) ◽

pp. 629-647 ◽

Cited By ~ 2

Author(s):

Hi Jun Choe ◽

Joerg Wolf ◽

Minsuk Yang

Keyword(s):

Weak Solutions ◽

Velocity Gradient ◽

Stokes Equations ◽

Regularity Criterion ◽

Local Regularity ◽

Navier Stokes ◽

Suitable Weak Solutions ◽

Navier Stokes Equations

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On regularity criteria for the Navier–Stokes equations based on one directional derivative of the velocity or one diagonal entry of the velocity gradient

Zeitschrift für angewandte Mathematik und Physik ◽

10.1007/s00033-020-01442-1 ◽

2021 ◽

Vol 72 (1) ◽

Author(s):

Zujin Zhang ◽

Yali Zhang

Keyword(s):

Velocity Gradient ◽

Stokes Equations ◽

Directional Derivative ◽

Diagonal Entry ◽

Regularity Criteria ◽

Navier Stokes ◽

Navier Stokes Equations

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On a regularity criterion for the Navier–Stokes equations involving gradient of one velocity component

Journal of Mathematical Physics ◽

10.1063/1.3268589 ◽

2009 ◽

Vol 50 (12) ◽

pp. 123514 ◽

Cited By ~ 54

Author(s):

Yong Zhou ◽

Milan Pokorný

Keyword(s):

Velocity Component ◽

Stokes Equations ◽

Regularity Criterion ◽

Navier Stokes ◽

Navier Stokes Equations

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The regularity criterion for the 3D Navier–Stokes equations involving end-point Prodi–Serrin type conditions

Applied Mathematics Letters ◽

10.1016/j.aml.2017.06.014 ◽

2018 ◽

Vol 75 ◽

pp. 37-42 ◽

Cited By ~ 2

Author(s):

Chenyin Qian

Keyword(s):

Stokes Equations ◽

Regularity Criterion ◽

Navier Stokes ◽

Navier Stokes Equations ◽

End Point

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Regularity Criterion for Weak Solutions to the Navier-Stokes Equations in Terms of the Gradient of the Pressure

Journal of Inequalities and Applications ◽

10.1155/2008/412678 ◽

2008 ◽

Vol 2008 (1) ◽

pp. 412678 ◽

Cited By ~ 9

Author(s):

Jishan Fan ◽

Tohru Ozawa

Keyword(s):

Weak Solutions ◽

Stokes Equations ◽

Regularity Criterion ◽

Navier Stokes ◽

Navier Stokes Equations

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