The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations

Hideo Kozono, Takayoshi Ogawa, Yasushi Taniuchi

Research output: Contribution to journalArticle

206 Citations (Scopus)

Abstract

We show the critical Sobolev inequalities in the Besov spaces with the logarithmic form such as Brezis-Gallouet-Wainger and Beale-Kato-Majda. As an application of those inequalities, the regularity problem under the critical condition to the Navier-Stokes equations, the Euler equations in and the gradient flow to the harmonic map to the sphere are discussed. Namely the Serrin-Ohyama type regularity criteria are improved in the terms of the Besov spaces.

Original languageEnglish
Pages (from-to)251-278
Number of pages28
JournalMathematische Zeitschrift
Volume242
Issue number2
DOIs
Publication statusPublished - 2002 Dec 1

ASJC Scopus subject areas

  • Mathematics(all)

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