Interior regularity criteria in weak spaces for the Navier-Stokes equations

Hyunseok Kim, Hideo Kozono

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

We study the interior regularity of weak solutions of the incompressible Navier-Stokes equations in Ω × (0, T), where Ω ⊂ R 3 and 0 < T < ∞. The local boundedness of a weak solution u is proved under the assumption that ||u||Lw s(0, T; Lw r (Ω)) is sufficiently small for some (r, s) with 2/s + 3/r = 1 and 3 ≤ r ≤ ∞. Our result extends the well-known criteria of Serrin (1962), Struwe (1988) and Takahashi (1990) to the weak space-time spaces.

Original languageEnglish
Pages (from-to)85-100
Number of pages16
JournalManuscripta Mathematica
Volume115
Issue number1
DOIs
Publication statusPublished - 2004 Sep
Externally publishedYes

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Regularity Criterion
Weak Solution
Navier-Stokes Equations
Interior
Incompressible Navier-Stokes Equations
Boundedness
Space-time
Regularity

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Interior regularity criteria in weak spaces for the Navier-Stokes equations. / Kim, Hyunseok; Kozono, Hideo.

In: Manuscripta Mathematica, Vol. 115, No. 1, 09.2004, p. 85-100.

Research output: Contribution to journalArticle

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