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

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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’s criterion (2007).

Original languageEnglish
Pages (from-to)629-647
Number of pages19
JournalMathematische Annalen
Volume370
Issue number1-2
DOIs
Publication statusPublished - 2018 Feb 1

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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