On the rate of decay of the oseen semigroup in exterior domains and its application to Navier-Stokes equation

Yuko Enomoto, Yoshihiro Shibata

Research output: Contribution to journalArticle

33 Citations (Scopus)

Abstract

We prove L p -L q estimates of the Oseen semigroup in n-dimensional exterior domains $$(n\,\geqslant\, 3),$$ which refine and improve those obtained by Kobayashi and Shibata [15]. As an application, we give a globally in time stability theory for the stationary Navier-Stokes flow whose velocity at infinity is a non-zero constant vector. We thus extend the result of Shibata [21]. In particular, we find an optimal rate of convergence of solutions of the non-stationary problem to those of the corresponding stationary problem.

Original languageEnglish
Pages (from-to)339-367
Number of pages29
JournalJournal of Mathematical Fluid Mechanics
Volume7
Issue number3
DOIs
Publication statusPublished - 2005 Aug 1

Keywords

  • Exterior domain
  • L -L estimate
  • Oseen semigroup
  • Stability
  • Stationary solution

ASJC Scopus subject areas

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

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