Regularity criterion on weak solutions to the navier-stokes equations

Hideo Kozono, Hermann Sohr

研究成果: Article

41 引用 (Scopus)

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In a domain ω ⊂ Rn, consider a weak solution u of the Navier-Stokes equations in the class u ε L∞(0, T;Ln(ω)). If lim supt→t*-0 ||u(t)||nn-||u(t*)||nn is small at each point of t* ε (0, T), then u is regular on ω̄ × (0, T). As an application, we give a precise characterization of the singular time; i.e., we show that if a solution u of the Navier-Stokes equations is initially smooth and loses its regularity at some later time T* < T, then either lim supt→T*-0 ||u(t)||Ln(ω) = +∞, or u(t) oscillates in Ln(ω) around the weak limit wlimt→ T*-0 u(t) with sufficiently large amplitude. Furthermore, we prove that every weak solution u of bounded variation on (0, T) with values in Ln(ω) becomes regular.

元の言語English
ページ(範囲)535-554
ページ数20
ジャーナルAdvances in Differential Equations
2
発行部数4
出版物ステータスPublished - 1997 12 1

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ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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