The Navier–Stokes equations in exterior Lipschitz domains: Lp-theory

Patrick Tolksdorf*, Keiichi Watanabe

*この研究の対応する著者

研究成果: Article査読

3 被引用数 (Scopus)

抄録

We show that the Stokes operator defined on Lσp(Ω) for an exterior Lipschitz domain Ω⊂Rn (n≥3) admits maximal regularity provided that p satisfies |1/p−1/2|<1/(2n)+ε for some ε>0. In particular, we prove that the negative of the Stokes operator generates a bounded analytic semigroup on Lσp(Ω) for such p. In addition, Lp-Lq-mapping properties of the Stokes semigroup and its gradient with optimal decay estimates are obtained. This enables us to prove the existence of mild solutions to the Navier–Stokes equations in the critical space L(0,T;Lσ3(Ω)) (locally in time and globally in time for small initial data).

本文言語English
ページ(範囲)5765-5801
ページ数37
ジャーナルJournal of Differential Equations
269
7
DOI
出版ステータスPublished - 2020 9月 15

ASJC Scopus subject areas

  • 分析
  • 応用数学

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