### 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 language | English |
---|---|

Pages (from-to) | 339-367 |

Number of pages | 29 |

Journal | Journal of Mathematical Fluid Mechanics |

Volume | 7 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2005 Aug |

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### 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.

Research output: Contribution to journal › Article

*Journal of Mathematical Fluid Mechanics*, vol. 7, no. 3, pp. 339-367. https://doi.org/10.1007/s00021-004-0132-8

}

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

AN - SCOPUS:24044519393

VL - 7

SP - 339

EP - 367

JO - Journal of Mathematical Fluid Mechanics

JF - Journal of Mathematical Fluid Mechanics

SN - 1422-6928

IS - 3

ER -