On the stationary Navier-Stokes equations in exterior domains

Hyunseok Kim, Hideo Kozono*

*この研究の対応する著者

研究成果: Article査読

7 被引用数 (Scopus)

抄録

This paper is concerned with the existence and uniqueness questions on weak solutions of the stationary Navier-Stokes equations in an exterior domain Ω in R3, where the external force is given by divF with F=F(x)=(Fji(x))i,j=1,2,3. First, we prove the existence and uniqueness of a weak solution for F∈L 3/2,∞(Ω)∩L p,q(Ω) with 3/2<p<3 and 1≤q≤∞ provided ||F||L3/2,∞(Ω) is sufficiently small. Here L p,q(Ω) denotes the well-known Lorentz space. We next show that weak solutions satisfying the energy inequality are unique for F∈L 3/2,∞(Ω)∩L 2(Ω) under the same smallness condition on ||F||L3/2,∞(Ω). This result provides a complete answer to the uniqueness question of weak solutions satisfying the energy inequality, the existence of which was proved by Leray in 1933. Finally, we establish the existence of weak solutions for data F in a very large class, for instance, in L 3/2(Ω)+L 2(Ω), which generalizes Leray's existence result.

本文言語English
ページ(範囲)486-495
ページ数10
ジャーナルJournal of Mathematical Analysis and Applications
395
2
DOI
出版ステータスPublished - 2012 11 15

ASJC Scopus subject areas

  • 分析
  • 応用数学

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