On the Stokes operator in general unbounded domains

Reinhard Farwig, Hideo Kozono, Hermann Sohr

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)111-136
Number of pages26
JournalHokkaido Mathematical Journal
Volume38
Issue number1
DOIs
Publication statusPublished - 2009 Jan 1

Keywords

  • Domains of uniform c-type
  • General unbounded domains
  • Maximal regularity
  • Stokes operator
  • Stokes resolvent
  • Stokes semigroup

ASJC Scopus subject areas

  • Mathematics(all)

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