### Abstract

Consider a body, B, rotating with constant angular velocity ω and fully submerged in a Navier-Stokes liquid that fills the whole space exterior to B. We analyze the flow of the liquid that is steady with respect to a frame attached to B. Our main theorem shows that the velocity field u of any weak solution (u p) in the sense of Leray has an asymptotic expansion with a suitable Landau solution as leading term and a remainder decaying pointwise like 1/ (x(^{1+α}as (x(→∞for any α.∈(0,1), provided the magnitude of ω is below a positive constant depending on α.We also furnish analogous expansions for ▶u and for the corresponding pressure field p. These results improve and clarify a recent result of R. Farwig and T. Hishida.

Original language | English |
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Pages (from-to) | 367-382 |

Number of pages | 16 |

Journal | Pacific Journal of Mathematics |

Volume | 253 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2011 |

Externally published | Yes |

### Keywords

- Asymptotic behavior of solutions
- Navier-Stokes equations
- Rotating frame

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

*Pacific Journal of Mathematics*,

*253*(2), 367-382. https://doi.org/10.2140/pjm.2011.253.367