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

Hyunseok Kim, Hideo Kozono

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25 Citations (Scopus)


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||Lws(0, T; Lwr (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
Issue number1
Publication statusPublished - 2004 Sep 1


ASJC Scopus subject areas

  • Mathematics(all)

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