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Science China Mathematics

, Volume 62, Issue 6, pp 1175–1204 | Cite as

Global strong solutions to 3-D Navier-Stokes system with strong dissipation in one direction

  • Marius Paicu
  • Ping ZhangEmail author
Articles
  • 23 Downloads

Abstract

We consider three-dimensional incompressible Navier-Stokes equations (NS) with different viscous coefficients in the vertical and horizontal variables. In particular, when one of these viscous coefficients is large enough compared with the initial data, we prove the global well-posedness of this system. In fact, we obtain the existence of a global strong solution to (NS) when the initial data verifies an anisotropic smallness condition which takes into account the different roles of the horizontal and vertical viscosity.

Keywords

anisotropic Navier-Stokes equations Littlewood-Paley theory well-posedness 

MSC(2010)

35Q30 76D03 

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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institut de Mathématiques de BordeauxUniversité Bordeaux 1BordeauxFrance
  2. 2.Academy of Mathematics and Systems Science and Hua Loo-Keng Key Laboratory of MathematicsChinese Academy of SciencesBeijingChina
  3. 3.School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijingChina

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