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Journal of Mathematical Fluid Mechanics

, Volume 13, Issue 3, pp 341–353 | Cite as

On Anisotropic Regularity Criteria for the Solutions to 3D Navier–Stokes Equations

  • Patrick PenelEmail author
  • Milan Pokorný
Article

Abstract

In this short note we consider the 3D Navier–Stokes equations in the whole space, for an incompressible fluid. We provide sufficient conditions for the regularity of strong solutions in terms of certain components of the velocity gradient. Based on the recent results from Kukavica (J Math Phys 48(6):065203, 2007) we show these conditions as anisotropic regularity criteria which partially interpolate results from Kukavica (J Math Phys 48(6):065203, 2007) and older results of similar type from Penel and Pokorný (Appl Math 49(5):483–493, 2004).

Mathematics Subject Classification (2010)

Primary 35Q30 Secondary 76D05 

Keywords

Incompressible Navier–Stokes equations regularity of solution regularity criteria 

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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  1. 1.Mathématique et labo. SNCUniversité du Sud, Toulon-VarLa Garde CedexFrance
  2. 2.Mathematical Institute of Charles UniversityPraha 8Czech Republic

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