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

Dongho Chae, Kyungkeun Kang, Jihoon Lee

Research output: Contribution to journalArticle

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

Fingerprint

Suitable Weak Solutions
Vorticity
Navier Stokes equations
Navier-Stokes Equations
Interior
Regularity
Regularity Criterion
Triebel-Lizorkin Space
Interior Point
Integrability

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

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On the interior regularity of suitable weak solutions to the Navier-Stokes equations. / Chae, Dongho; Kang, Kyungkeun; Lee, Jihoon.

In: Communications in Partial Differential Equations, Vol. 32, No. 8, 01.08.2007, p. 1189-1207.

Research output: Contribution to journalArticle

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AB - 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.

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