## Abstract

We investigate the existence, uniqueness and regularity of time-periodic solutions to the Navier-Stokes equations governing the flow of a viscous liquid past a three-dimensional body moving with a time-periodic translational velocity. The net motion of the body over a full time-period is assumed to be non-zero. In this case, the appropriate linearization is the time-periodic Oseen system in a three-dimensional exterior domain. A priori L^{q} estimates are established for this linearization. Based on these “maximal regularity” estimates, the existence and uniqueness of smooth solutions to the fully nonlinear Navier-Stokes problem is obtained by the contraction mapping principle.

Original language | English |
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Title of host publication | Partial Differential Equations in Fluid Mechanics |

Publisher | Cambridge University Press |

Pages | 20-49 |

Number of pages | 30 |

ISBN (Electronic) | 9781108610575 |

ISBN (Print) | 9781108460965 |

DOIs | |

Publication status | Published - 2019 Jan 1 |

Externally published | Yes |

## Keywords

- A priori estimates
- Exterior domain
- Navier-Stokes
- Time-periodic Oseen system
- Viscous liquid past a body

## ASJC Scopus subject areas

- Mathematics(all)