Regularity of weak solutions for the Navier-Stokes equations via energy criteria

Reinhard Farwig*, Hideo Kozono, Hermann Sohr

*この研究の対応する著者

研究成果: Conference contribution

2 被引用数 (Scopus)

抄録

Consider a weak solution u of the instationary Navier-Stokes system in a bounded domain of R3 satisfying the strong energy inequality. Extending previous results by Farwig et al., J. Math. Fluid Mech. 11, 1-14 (2008), we prove among other things that u is regular if either the kinetic energy 1/2 ∥u(t) ∥22 or the dissipation energy ∫ t 0 ∥∇u(τ ) ∥2 2 dτ is (left-side) Hölder continuous as a function of time t with Hölder exponent 1/2 and with sufficiently small Hölder seminorm. The proofs use local regularity results which are based on the theory of very weak solutions and on uniqueness arguments for weak solutions.

本文言語English
ホスト出版物のタイトルAdvances in Mathematical Fluid Mechanics - Dedicated to Giovanni Paolo Galdi on the Occasion of His 60th Birthday
出版社Springer Verlag
ページ215-227
ページ数13
ISBN(印刷版)9783642040672
DOI
出版ステータスPublished - 2010
外部発表はい
イベント2007 International Conference on Mathematical Fluid Mechanics - Estoril, Portugal
継続期間: 2007 5 212007 5 25

出版物シリーズ

名前Advances in Mathematical Fluid Mechanics - Dedicated to Giovanni Paolo Galdi on the Occasion of His 60th Birthday

Conference

Conference2007 International Conference on Mathematical Fluid Mechanics
国/地域Portugal
CityEstoril
Period07/5/2107/5/25

ASJC Scopus subject areas

  • 流体および伝熱
  • 数学 (全般)

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