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

197 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
Externally publishedYes

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Semilinear Evolution Equation
Regularity Criterion
Sobolev Inequality
Besov Spaces
Gradient Flow
Harmonic Maps
Euler Equations
Navier-Stokes Equations
Logarithmic
Regularity
Term
Form

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations. / Kozono, Hideo; Ogawa, Takayoshi; Taniuchi, Yasushi.

In: Mathematische Zeitschrift, Vol. 242, No. 2, 2002, p. 251-278.

Research output: Contribution to journalArticle

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