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

Dongho Chae; Kyungkeun Kang; Jihoon Lee

doi:10.1080/03605300601088823

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

Dongho Chae, Kyungkeun Kang, Jihoon Lee

Department of Mathematics

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

32 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 language	English
Pages (from-to)	1189-1207
Number of pages	19
Journal	Communications in Partial Differential Equations
Volume	32
Issue number	8
DOIs	https://doi.org/10.1080/03605300601088823
Publication status	Published - 2007 Aug

Bibliographical note

Funding Information:
This research is supported partially by KOSEF grant no. R01-2005-000-10077-0. D. Chae is supported by KRF Grant (MOEHRD, Basic Research Promotion Fund). K. Kang is supported by KRF-2006-331-C00020. J. Lee is supported by KRF-2006-311-C00007.

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1080/03605300601088823

Cite this

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title = "On the interior regularity of suitable weak solutions to the Navier-Stokes equations",

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.",

author = "Dongho Chae and Kyungkeun Kang and Jihoon Lee",

note = "Funding Information: This research is supported partially by KOSEF grant no. R01-2005-000-10077-0. D. Chae is supported by KRF Grant (MOEHRD, Basic Research Promotion Fund). K. Kang is supported by KRF-2006-331-C00020. J. Lee is supported by KRF-2006-311-C00007.",

year = "2007",

month = aug,

doi = "10.1080/03605300601088823",

language = "English",

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AU - Chae, Dongho

AU - Kang, Kyungkeun

AU - Lee, Jihoon

N1 - Funding Information: This research is supported partially by KOSEF grant no. R01-2005-000-10077-0. D. Chae is supported by KRF Grant (MOEHRD, Basic Research Promotion Fund). K. Kang is supported by KRF-2006-331-C00020. J. Lee is supported by KRF-2006-311-C00007.

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N2 - 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.

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

Abstract

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