On the interior regularity of suitable weak solutions to the Navier-Stokes equations

Dongho Chae, Kyungkeun Kang, Jihoon Lee

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27 Citations (Scopus)

Abstract

We obtain the interior regularity criteria for the vorticity of "suitable" weak solutions to the Navier-Stokes equations. We prove that if two components of a vorticiy belongs to [image omitted] in a neighborhood of an interior point with 3/p+2/q2 and 3/2p, then solution is regular near that point. We also show that if the direction field of the vorticity is in some Triebel-Lizorkin spaces and the vorticity magnitude satisfies an appropriate integrability condition in a neighborhood of a point, then solution is regular near that point.

Original languageEnglish
Pages (from-to)1189-1207
Number of pages19
JournalCommunications in Partial Differential Equations
Volume32
Issue number8
DOIs
Publication statusPublished - 2007 Aug 1

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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