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

Reinhard Farwig, Hideo Kozono, Hermann Sohr

研究成果: Conference contribution

1 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
ページ215-227
ページ数13
DOI
出版ステータスPublished - 2010 12 1
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
CountryPortugal
CityEstoril
Period07/5/2107/5/25

ASJC Scopus subject areas

  • Fluid Flow and Transfer Processes

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