### Abstract

Consider the Navier-Stokes fluid filling the whole 3-dimensional space exterior to a rotating obstacle with constant angular velocity ω. By using a coordinate system attached to the obstacle, the problem is reduced to an equivalent one in a fixed exterior domain. It is proved that the reduced problem possesses a unique global solution which goes to a stationary flow as t → ∞ when ω and the initial disturbance are small in a sense.

Original language | English |
---|---|

Pages (from-to) | 303-307 |

Number of pages | 5 |

Journal | WSEAS Transactions on Mathematics |

Volume | 5 |

Issue number | 3 |

Publication status | Published - 2006 Mar |

### Fingerprint

### Keywords

- Decay
- Exterior domain
- Global solution
- Navier-Stokes flow
- Rotating body
- Stability

### ASJC Scopus subject areas

- Mathematics (miscellaneous)
- Computational Mathematics
- Computer Science (miscellaneous)

### Cite this

*WSEAS Transactions on Mathematics*,

*5*(3), 303-307.

**Globally in time existence theorem for the Navier-Stokes flow in the exterior of a rotating obstacle.** / Hishida, Toshiaki; Shibata, Yoshihiro.

Research output: Contribution to journal › Article

*WSEAS Transactions on Mathematics*, vol. 5, no. 3, pp. 303-307.

}

TY - JOUR

T1 - Globally in time existence theorem for the Navier-Stokes flow in the exterior of a rotating obstacle

AU - Hishida, Toshiaki

AU - Shibata, Yoshihiro

PY - 2006/3

Y1 - 2006/3

N2 - Consider the Navier-Stokes fluid filling the whole 3-dimensional space exterior to a rotating obstacle with constant angular velocity ω. By using a coordinate system attached to the obstacle, the problem is reduced to an equivalent one in a fixed exterior domain. It is proved that the reduced problem possesses a unique global solution which goes to a stationary flow as t → ∞ when ω and the initial disturbance are small in a sense.

AB - Consider the Navier-Stokes fluid filling the whole 3-dimensional space exterior to a rotating obstacle with constant angular velocity ω. By using a coordinate system attached to the obstacle, the problem is reduced to an equivalent one in a fixed exterior domain. It is proved that the reduced problem possesses a unique global solution which goes to a stationary flow as t → ∞ when ω and the initial disturbance are small in a sense.

KW - Decay

KW - Exterior domain

KW - Global solution

KW - Navier-Stokes flow

KW - Rotating body

KW - Stability

UR - http://www.scopus.com/inward/record.url?scp=33744543464&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33744543464&partnerID=8YFLogxK

M3 - Article

VL - 5

SP - 303

EP - 307

JO - WSEAS Transactions on Mathematics

JF - WSEAS Transactions on Mathematics

SN - 1109-2769

IS - 3

ER -