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

Hideo Kozono; Takayoshi Ogawa; Yasushi Taniuchi

doi:10.1007/s002090100332

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

Hideo Kozono^*, Takayoshi Ogawa, Yasushi Taniuchi

^*この研究の対応する著者

研究成果: Article › 査読

249 被引用数 (Scopus)

抄録

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.

本文言語	English
ページ（範囲）	251-278
ページ数	28
ジャーナル	Mathematische Zeitschrift
巻	242
号	2
DOI	https://doi.org/10.1007/s002090100332
出版ステータス	Published - 2002 12月 1
外部発表	はい

ASJC Scopus subject areas

数学 (全般)

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10.1007/s002090100332

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AB - 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.

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

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