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ANNALI DELL'UNIVERSITA' DI FERRARA

, Volume 63, Issue 2, pp 353–363 | Cite as

A regularity criterion for 3D Navier–Stokes equations via one component of velocity and vorticity

  • Myong-Hwan Ri
Article
  • 98 Downloads

Abstract

In this paper we show that a Leray–Hopf weak solution u to 3D Navier–Stokes initial value problem is smooth if there is some \(\alpha \in {{{\mathbb {R}}}}, \alpha \ne 0,\) such that \(\alpha u_3+(-\Delta )^{-1/2}\omega _3\) is suitably smooth, where \(\omega =\text {curl}\,u\).

Keywords

Navier–Stokes equations Global regularity 

Mathematics Subject Classification

35Q30 35B35 

Notes

Acknowledgements

The author is grateful to Prof. Reinhard Farwig for his proof of Lemma 4.1 given in this article, which is much more elegant than the author’s former one.

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Copyright information

© Università degli Studi di Ferrara 2017

Authors and Affiliations

  1. 1.Institute of MathematicsState Academy of SciencesPyongyangDemocratic People’s Republic of Korea

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