Energy-based regularity criteria for the Navier-Stokes equations

Reinhard Farwig, Hideo Kozono, Hermann Sohr

研究成果: Article査読

11 被引用数 (Scopus)

抄録

We present several new regularity criteria for weak solutions u of the instationary Navier-Stokes system which additionally satisfy the strong energy inequality. (i) If the kinetic energy 1/2|u(t)\|22 is Hölder continuous as a function of time t with Hölder exponent α in (1/2, 1), then u is regular. (ii) If for some α in (1/2, 1) the dissipation energy satisfies the left-side condition lim rm inf δrightarrow 01δα int-δt∇ u 22dτ <∞ for all t of the given time interval, then u is regular. The proofs use local regularity results which are based on the theory of very weak solutions, see [1], [4], and on uniqueness arguments for weak solutions. Finally, in the last section we mention a local space-time regularity condition.

本文言語English
ページ(範囲)428-442
ページ数15
ジャーナルJournal of Mathematical Fluid Mechanics
11
3
DOI
出版ステータスPublished - 2009 10

ASJC Scopus subject areas

  • 数理物理学
  • 凝縮系物理学
  • 計算数学
  • 応用数学

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