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

32 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
Externally publishedYes

Fingerprint

Stokes flow
Navier-Stokes equations
Flow velocity
Navier-Stokes equation
flow velocity
infinity
Navier Stokes equations
decay
estimates
rate

Keywords

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

ASJC Scopus subject areas

  • Materials Science (miscellaneous)
  • Oceanography
  • Fluid Flow and Transfer Processes
  • Applied Mathematics

Cite this

On the rate of decay of the oseen semigroup in exterior domains and its application to Navier-Stokes equation. / Enomoto, Yuko; Shibata, Yoshihiro.

In: Journal of Mathematical Fluid Mechanics, Vol. 7, No. 3, 08.2005, p. 339-367.

Research output: Contribution to journalArticle

@article{ae2342f416ef4bfe9787e894cdc8dc77,
title = "On the rate of decay of the oseen semigroup in exterior domains and its application to Navier-Stokes equation",
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.",
keywords = "Exterior domain, L -L estimate, Oseen semigroup, Stability, Stationary solution",
author = "Yuko Enomoto and Yoshihiro Shibata",
year = "2005",
month = "8",
doi = "10.1007/s00021-004-0132-8",
language = "English",
volume = "7",
pages = "339--367",
journal = "Journal of Mathematical Fluid Mechanics",
issn = "1422-6928",
publisher = "Birkhauser Verlag Basel",
number = "3",

}

TY - JOUR

T1 - On the rate of decay of the oseen semigroup in exterior domains and its application to Navier-Stokes equation

AU - Enomoto, Yuko

AU - Shibata, Yoshihiro

PY - 2005/8

Y1 - 2005/8

N2 - 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.

AB - 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.

KW - Exterior domain

KW - L -L estimate

KW - Oseen semigroup

KW - Stability

KW - Stationary solution

UR - http://www.scopus.com/inward/record.url?scp=24044519393&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=24044519393&partnerID=8YFLogxK

U2 - 10.1007/s00021-004-0132-8

DO - 10.1007/s00021-004-0132-8

M3 - Article

VL - 7

SP - 339

EP - 367

JO - Journal of Mathematical Fluid Mechanics

JF - Journal of Mathematical Fluid Mechanics

SN - 1422-6928

IS - 3

ER -