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

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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