On boundary regularity of the Navier-Stokes equations

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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 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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All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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