Maximal L p - L q -Estimates for the stokes equation: A short proof of solonnikov's theorem

Matthias Geissert, Matthias Hess, Matthias Georg Hieber, Céline Schwarz, Kyriakos Stavrakidis

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

Introducing a new localization method involving Bogovskis operator we give a short and new proof for maximal L p - L q -estimates for the solution of the Stokes equation. Moreover, it is shown that, up to constants, the Stokes operator is an {\mathcal{R}} -sectorial operator in L{p}{\sigma}(\Omega), 1 <p <\infty, of {\mathcal{R}} -angle 0, for bounded or exterior domains of Ω.

Original languageEnglish
Pages (from-to)47-60
Number of pages14
JournalJournal of Mathematical Fluid Mechanics
Volume12
Issue number1
DOIs
Publication statusPublished - 2010 Mar
Externally publishedYes

Keywords

  • Exterior domains
  • Maximal L - L -estimates
  • Stokes equation

ASJC Scopus subject areas

  • Applied Mathematics
  • Mathematical Physics
  • Computational Mathematics
  • Condensed Matter Physics

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