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Mathematische Annalen

, Volume 370, Issue 1–2, pp 629–647 | Cite as

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

  • Hi Jun Choe
  • Joerg Wolf
  • Minsuk YangEmail author
Article

Abstract

We study the partial regularity of suitable weak solutions to the three dimensional incompressible Navier–Stokes equations. There have been several attempts to refine the Caffarelli–Kohn–Nirenberg criterion (1982). We present an improved version of the CKN criterion with a direct method, which also provides the quantitative relation in Seregin’s criterion (2007).

Mathematics Subject Classification

35Q35 35D30 35B65 

Notes

Acknowledgements

H. J. Choe has been supported by the National Reserch Foundation of Korea (NRF) grant, funded by the Korea government (MSIP) (No. 20151009350). J. Wolf has been supported by the German Research Foundation (DFG) through the project WO1988/1-1; 612414. M. Yang has been supported by the National Research Foundation of Korea(NRF) Grant funded by the Korea government (MSIP) (No. 2016R1C1B2015731).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of MathematicsYonsei UniversitySeoulRepublic of Korea
  2. 2.Department of MathematicsHumboldt University BerlinBerlinGermany
  3. 3.Korea Institute for Advanced StudySeoulRepublic of Korea

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