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 Yang

doi:10.1007/s00208-017-1522-6

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 Yang

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

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).

Original language	English
Pages (from-to)	629-647
Number of pages	19
Journal	Mathematische Annalen
Volume	370
Issue number	1-2
DOIs	https://doi.org/10.1007/s00208-017-1522-6
Publication status	Published - 2018 Feb 1

Bibliographical note

Funding Information:
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).

Publisher Copyright:
© 2017, Springer-Verlag Berlin Heidelberg.

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.1007/s00208-017-1522-6

Cite this

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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{\textquoteright}s criterion (2007).",

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AU - Wolf, Joerg

AU - Yang, Minsuk

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N2 - 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).

AB - 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).

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

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