## Abstract

The equations governing the flow of a viscous incompressible fluid around a rigid body that performs a prescribed time-periodic motion with constant axes of translation and rotation are investigated. Under the assumption that the period and the angular velocity of the prescribed rigid-body motion are compatible, and that the mean translational velocity is non-zero, existence of a time-periodic solution is established. The proof is based on an appropriate linearization, which is examined within a setting of absolutely convergent Fourier series. Since the corresponding resolvent problem is ill-posed in classical Sobolev spaces, a linear theory is developed in a framework of homogeneous Sobolev spaces.

Original language | English |
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Article number | 28 |

Journal | Journal of Mathematical Fluid Mechanics |

Volume | 23 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2021 Feb |

## Keywords

- Navier-Stokes
- Oseen flow
- Rotating obstacles
- Time-periodic solutions

## ASJC Scopus subject areas

- Mathematical Physics
- Condensed Matter Physics
- Computational Mathematics
- Applied Mathematics