On boundary regularity of the Navier-Stokes equations

Kyungkeun Kang

doi:10.1081/PDE-200033743

On boundary regularity of the Navier-Stokes equations

Kyungkeun Kang

Department of Mathematics

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

21 Citations (Scopus)

Abstract

We study boundary regularity of weak solutions of the Navier-Stokes equations in the half-space in dimension n ≥ 3. We prove that a weak solution u which is locally in the class L^p,q with 2/p + n/q = 1, q > n near boundary is Hölder continuous up to the boundary. Our main tool is a pointwise estimate for the fundamental solution of the Stokes system, which is of independent interest.

Original language	English
Pages (from-to)	955-987
Number of pages	33
Journal	Communications in Partial Differential Equations
Volume	29
Issue number	7-8
DOIs	https://doi.org/10.1081/PDE-200033743
Publication status	Published - 2004 Jul

Bibliographical note

Funding Information:
The author was supported in part by NSF Grant No. DMS-9877055. The author is deeply grateful to Professor Vladimïr Sˇverák for guidance and encouragement. The author thanks Professor G. Seregin for showing him the preprint of the paper Seregin (2002) and Professor V. Solonnikov for drawing his attention to the papers (Solonnikov, 1973, 1978). The author also thanks the referee for his/her valuable comments.

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1081/PDE-200033743

Cite this

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abstract = "We study boundary regularity of weak solutions of the Navier-Stokes equations in the half-space in dimension n ≥ 3. We prove that a weak solution u which is locally in the class Lp,q with 2/p + n/q = 1, q > n near boundary is H{\"o}lder continuous up to the boundary. Our main tool is a pointwise estimate for the fundamental solution of the Stokes system, which is of independent interest.",

author = "Kyungkeun Kang",

note = "Funding Information: The author was supported in part by NSF Grant No. DMS-9877055. The author is deeply grateful to Professor Vladim{\"i}r Sˇver{\'a}k for guidance and encouragement. The author thanks Professor G. Seregin for showing him the preprint of the paper Seregin (2002) and Professor V. Solonnikov for drawing his attention to the papers (Solonnikov, 1973, 1978). The author also thanks the referee for his/her valuable comments.",

year = "2004",

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AU - Kang, Kyungkeun

N1 - Funding Information: The author was supported in part by NSF Grant No. DMS-9877055. The author is deeply grateful to Professor Vladimïr Sˇverák for guidance and encouragement. The author thanks Professor G. Seregin for showing him the preprint of the paper Seregin (2002) and Professor V. Solonnikov for drawing his attention to the papers (Solonnikov, 1973, 1978). The author also thanks the referee for his/her valuable comments.

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N2 - We study boundary regularity of weak solutions of the Navier-Stokes equations in the half-space in dimension n ≥ 3. We prove that a weak solution u which is locally in the class Lp,q with 2/p + n/q = 1, q > n near boundary is Hölder continuous up to the boundary. Our main tool is a pointwise estimate for the fundamental solution of the Stokes system, which is of independent interest.

AB - We study boundary regularity of weak solutions of the Navier-Stokes equations in the half-space in dimension n ≥ 3. We prove that a weak solution u which is locally in the class Lp,q with 2/p + n/q = 1, q > n near boundary is Hölder continuous up to the boundary. Our main tool is a pointwise estimate for the fundamental solution of the Stokes system, which is of independent interest.

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JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

IS - 7-8

ER -

On boundary regularity of the Navier-Stokes equations

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

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