Improvement of some anisotropic regularity criteria for the Navier--Stokes equations

Patrick Penel; Milan Pokorný

doi:10.3934/dcdss.2013.6.1401

Article Contents

2013, Volume 6, Issue 5: 1401-1407. Doi: 10.3934/dcdss.2013.6.1401

This issue Previous Article A note on local interior regularity of a suitable weak solution to the Navier--Stokes problem Next Article Analytic rates of solutions to the Euler equations

Improvement of some anisotropic regularity criteria for the Navier--Stokes equations

Patrick Penel^1, and
Milan Pokorný^2,

1.
Mathématique et Laboratoire SNC, Université du Sud, Toulon-Var, BP 20132, 83957 La Garde Cedex
2.
Mathematical Institute of Charles University, Sokolovská 83, 186 75 Praha 8

Received: November 2011

Revised: February 2012

Published: October 2013

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Abstract

We consider the incompressible Navier--Stokes equations in the entire three-dimensional space. Assuming additional regularity on the components of the vector field $\partial_3$u we show intermediate anisotropic regularity results between the results by Kukavica and Ziane [5] and by Cao and Titi [3]and improve the result from the paper by Penel and Pokorný [9].

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Mathematics Subject Classification: Primary: 35Q30; Secondary: 76D05.

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References

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