Resolvent Estimates in L p for the Stokes Operator in Lipschitz Domains

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30 Scopus citations

Abstract

We establish the L p resolvent estimates for the Stokes operator in Lipschitz domains in ℝ d, d ≥ 3 for {pipe}1/p-1/2{pipe} < 1/2d + εThe result implies that the Stokes operator in a three-dimensional Lipschitz domain generates a bounded analytic semigroup in L p for (3/2) - ε < p < 3 + ε. This gives an affirmative answer to a conjecture of M. Taylor (Progr. Nonlinear Differential Equations Appl., vol. 42, pp. 320-334).

Original languageEnglish
Pages (from-to)395-424
Number of pages30
JournalArchive for Rational Mechanics and Analysis
Volume205
Issue number2
DOIs
StatePublished - Aug 2012

Bibliographical note

Funding Information:
Supported in part by NSF grant DMS-0855294.

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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