A regularity criterion for the Navier-Stokes equations

Hyeong Ohk Bae; Hi Jun Choe

doi:10.1080/03605300701257500

A regularity criterion for the Navier-Stokes equations

Hyeong Ohk Bae, Hi Jun Choe

Department of Mathematics

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

34 Citations (Scopus)

Abstract

We prove that a weak solution u=(u1, u2, u3) to the Navier-Stokes equations is strong, if any two components of u satisfy Prodi-Ohyama-Serrin's criterion. As a local regularity criterion, we prove u is bounded locally if any two components of the velocity lie in L6,.

Original language	English
Pages (from-to)	1173-1187
Number of pages	15
Journal	Communications in Partial Differential Equations
Volume	32
Issue number	7
DOIs	https://doi.org/10.1080/03605300701257500
Publication status	Published - 2007 Jul

Bibliographical note

Funding Information:
This work was supported by the Korea Research Foundation Grant (MOEHRD, Basic Research Promotion Fund) (KRF-2006-312-C00466).

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1080/03605300701257500

Cite this

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abstract = "We prove that a weak solution u=(u1, u2, u3) to the Navier-Stokes equations is strong, if any two components of u satisfy Prodi-Ohyama-Serrin's criterion. As a local regularity criterion, we prove u is bounded locally if any two components of the velocity lie in L6,.",

author = "Bae, {Hyeong Ohk} and Choe, {Hi Jun}",

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N2 - We prove that a weak solution u=(u1, u2, u3) to the Navier-Stokes equations is strong, if any two components of u satisfy Prodi-Ohyama-Serrin's criterion. As a local regularity criterion, we prove u is bounded locally if any two components of the velocity lie in L6,.

AB - We prove that a weak solution u=(u1, u2, u3) to the Navier-Stokes equations is strong, if any two components of u satisfy Prodi-Ohyama-Serrin's criterion. As a local regularity criterion, we prove u is bounded locally if any two components of the velocity lie in L6,.

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A regularity criterion for the Navier-Stokes equations

Abstract

Bibliographical note

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