Removable singularities of weak solutions to the Navier-Stokes equations

Hideo Kozono*

*この研究の対応する著者

研究成果: Article査読

26 被引用数 (Scopus)

抄録

Consider the Navier-Stokes equations in Ω × (0,T), where Ω is a domain in R3. We show that there is an absolute constant ε0 such that every weak solution u with the property that supt∈(a,b) ∥u(t)∥L3W(D) ≤ ε0 is necessarily of class C in the space-time variables on any compact subset of D x (a, b), where D ⊂⊂ Ω and 0 < a < b < T. As an application, we prove that if the weak solution u behaves around (x0, t0) ∈ Ω × (0,T) like u(x,t) = 0(|x - x0l-1) as x → x0 uniformly in t in some neighbourhood of t0, then (x0,t0) is actually a removable singularity of u.

本文言語English
ページ(範囲)949-966
ページ数18
ジャーナルCommunications in Partial Differential Equations
23
5-6
DOI
出版ステータスPublished - 1998 1 1
外部発表はい

ASJC Scopus subject areas

  • 分析
  • 応用数学

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