### 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 |
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Pages (from-to) | 303-307 |

Number of pages | 5 |

Journal | WSEAS Transactions on Mathematics |

Volume | 5 |

Issue number | 3 |

Publication status | Published - 2006 Mar 1 |

### Keywords

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

### ASJC Scopus subject areas

- Algebra and Number Theory
- Endocrinology, Diabetes and Metabolism
- Statistics and Probability
- Discrete Mathematics and Combinatorics
- Management Science and Operations Research
- Control and Optimization
- Computational Mathematics
- Applied Mathematics

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## Cite this

Hishida, T., & Shibata, Y. (2006). Globally in time existence theorem for the Navier-Stokes flow in the exterior of a rotating obstacle.

*WSEAS Transactions on Mathematics*,*5*(3), 303-307.