On the Stokes operator in general unbounded domains

Reinhard Farwig, Hideo Kozono, Hermann Sohr

研究成果: Article

21 引用 (Scopus)

抜粋

It is known that the Stokes operator is not well-defined in Lq-spaces for certain unbounded smooth domains unless q = 2. In this paper, we generalize a new approach to the Stokes resolvent problem and to maximal regularity in general un-bounded smooth domains from the three-dimensional case, see [7], to the n-dimensional one, n ≥ 2, replacing the space Lq, 1 < q < ∞, by L̃q where L̃q = L̃q ∩ L2 for q ≥ 2 and L̃q = Lq + L2 for 1 < q < 2. In particular, we show that the Stokes operator is well-defined in Lq for every unbounded domain of uniform C1,1-type in Rn, n ≥ 2, satisfies the classical resolvent estimate, generates an analytic semigroup and has maximal regularity.

元の言語English
ページ(範囲)111-136
ページ数26
ジャーナルHokkaido Mathematical Journal
38
発行部数1
DOI
出版物ステータスPublished - 2009 1 1
外部発表Yes

ASJC Scopus subject areas

  • Mathematics(all)

フィンガープリント On the Stokes operator in general unbounded domains' の研究トピックを掘り下げます。これらはともに一意のフィンガープリントを構成します。

  • これを引用