On boundary regularity of the Navier-Stokes equations

Research output: Contribution to journalArticle

20 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 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.

Original languageEnglish
Pages (from-to)955-987
Number of pages33
JournalCommunications in Partial Differential Equations
Volume29
Issue number7-8
DOIs
Publication statusPublished - 2004 Jul 1

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Boundary Regularity
Navier Stokes equations
Weak Solution
Navier-Stokes Equations
Stokes System
Pointwise Estimates
Fundamental Solution
Half-space
Class

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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.",
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On boundary regularity of the Navier-Stokes equations. / Kang, Kyungkeun.

In: Communications in Partial Differential Equations, Vol. 29, No. 7-8, 01.07.2004, p. 955-987.

Research output: Contribution to journalArticle

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