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

20 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

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Suitable Weak Solutions
Regularity Criterion
Navier Stokes equations
Navier-Stokes Equations
Less than or equal to
Partial Regularity
Integral Condition
Weak Solution
Three-dimension
Interior
Norm

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

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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 H{\"o}lder 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.",
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Regularity criteria for suitable weak solutions of the Navier-Stokes equations near the boundary. / Gustafson, Stephen; Kang, Kyungkeun; Tsai, Tai Peng.

In: Journal of Differential Equations, Vol. 226, No. 2, 15.07.2006, p. 594-618.

Research output: Contribution to journalArticle

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