Stokes resolvent estimates in spaces of bounded functions

Ken Abe, Yoshikazu Giga, Matthias Georg Hieber

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

The Stokes equation on a domain Ω Rn is well understood in the Lp-setting for a large class of domains including bounded and exterior domains with smooth boundaries pro- vided 1 <p <∞. The situation is very different for the case p = ∞ since in this case the Helmholtz projection does not act as a bounded operator anymore. Nevertheless it was recently proved by the first and the second author of this paper by a contradiction argument that the Stokes operator generates an analytic semigroup on spaces of bounded functions for a large class of domains. This paper presents a new approach as well as new a priori L-type estimates to the Stokes equation. They imply in par- ticular that the Stokes operator generates a C0-analytic semigroup of angle π/2 on C0,α(Ω), or a non- C0-analytic semigroup on Lα (Ω) for a large class of domains. The approach presented is inspired by the so called Masuda-Stewart technique for elliptic operators. It is shown furthermore that the method presented applies also to different types of boundary conditions as, e.g., Robin boundary conditions.

Original languageEnglish
Pages (from-to)537-559
Number of pages23
JournalAnnales Scientifiques de l'Ecole Normale Superieure
Volume48
Issue number3
Publication statusPublished - 2015 May 1
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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