### Abstract

We consider the motion of a viscous fluid filling the whole three-dimensional space exterior to a rotating obstacle with constant angular velocity. We develop the L estimate and the similar estimates in the Lorentz spaces of the Stokes semigroup with rotation effect. We next apply them to the Navier-Stokes equation to prove the global existence of a unique solution which goes to a stationary flow as t → ∞ with some definite rates when both the stationary flow and the initial disturbance are sufficiently small in L (weak-L .

Original language | English |
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Pages (from-to) | 339-421 |

Number of pages | 83 |

Journal | Archive for Rational Mechanics and Analysis |

Volume | 193 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2009 Aug |

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### ASJC Scopus subject areas

- Analysis
- Mechanical Engineering
- Mathematics (miscellaneous)