### 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)

### Cite this

**Lp-Lq estimate of the stokes operator and navier-stokes flows in the exterior of a rotating obstacle.** / Hishida, Toshiaki; Shibata, Yoshihiro.

Research output: Contribution to journal › Article

*Archive for Rational Mechanics and Analysis*, vol. 193, no. 2, pp. 339-421. https://doi.org/10.1007/s00205-008-0130-8

}

TY - JOUR

T1 - Lp-Lq estimate of the stokes operator and navier-stokes flows in the exterior of a rotating obstacle

AU - Hishida, Toshiaki

AU - Shibata, Yoshihiro

PY - 2009/8

Y1 - 2009/8

N2 - 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 .

AB - 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 .

UR - http://www.scopus.com/inward/record.url?scp=67650401463&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67650401463&partnerID=8YFLogxK

U2 - 10.1007/s00205-008-0130-8

DO - 10.1007/s00205-008-0130-8

M3 - Article

VL - 193

SP - 339

EP - 421

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

SN - 0003-9527

IS - 2

ER -