### 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 |
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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 1 |

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### Keywords

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

### ASJC Scopus subject areas

- Mathematical Physics
- Condensed Matter Physics
- Computational Mathematics
- Applied Mathematics