Regularity criteria for suitable weak solutions of the Navier-Stokes equations near the boundary

Stephen Gustafson, Kyungkeun Kang, Tai Peng Tsai

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

We present some new regularity criteria for "suitable weak solutions" of the Navier-Stokes equations near the boundary in dimension three. We prove that suitable weak solutions are Hölder continuous up to the boundary provided that the scaled mixed norm Lx, tp, q with 3 / p + 2 / q {less-than or slanted equal to} 2, 2 < q {less-than or slanted equal to} ∞, ( p, q ) ≠ ( 3 / 2, ∞ ) is small near the boundary. Our methods yield new results in the interior case as well. Partial regularity of weak solutions is also analyzed under some additional integral conditions.

Original languageEnglish
Pages (from-to)594-618
Number of pages25
JournalJournal of Differential Equations
Volume226
Issue number2
DOIs
Publication statusPublished - 2006 Jul 15

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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