### Abstract

We consider a body, B, that rotates, without translating, in a Navier-Stokes liquid that fills the whole space exterior to B. We analyze asymptotic properties of steady-state motions, that is, time-independent solutions to the equation of motion written in a frame attached to the body. We prove that “weak” steady-state solutions in the sense of J. Leray that satisfy the energy inequality are Physically Reasonable in the sense of R. Finn, provided the “size” of the data is suitably restricted.

Original language | English |
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Title of host publication | Progress in Nonlinear Differential Equations and Their Application |

Publisher | Springer US |

Pages | 251-266 |

Number of pages | 16 |

DOIs | |

Publication status | Published - 2011 |

Externally published | Yes |

### Publication series

Name | Progress in Nonlinear Differential Equations and Their Application |
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Volume | 80 |

ISSN (Print) | 1421-1750 |

ISSN (Electronic) | 2374-0280 |

### Keywords

- Asymptotic behavior
- Navier-Stokes equations
- Rotating body

### ASJC Scopus subject areas

- Analysis
- Computational Mechanics
- Mathematical Physics
- Control and Optimization
- Applied Mathematics

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## Cite this

Galdi, G. P., & Kyed, M. (2011). Asymptotic behavior of a Leray solution around a rotating obstacle. In

*Progress in Nonlinear Differential Equations and Their Application*(pp. 251-266). (Progress in Nonlinear Differential Equations and Their Application; Vol. 80). Springer US. https://doi.org/10.1007/978-3-0348-0075-4_13