### Abstract

We consider the Navier-Stokes equations with the Coriolis force when initial data may not decrease at spatial infinity so that almost periodic data is allowed. We prove that the local-in-time solution is analytic in time when initial data are in F M_{0}, the Fourier preimage of the space of all finite Radon measures with no point mass at the origin. When the initial data are almost periodic, this implies that the complex amplitude is analytic in time. In particular, a new mode cannot be created at any positive time.

Original language | English (US) |
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Pages (from-to) | 1422-1428 |

Number of pages | 7 |

Journal | Physica D: Nonlinear Phenomena |

Volume | 237 |

Issue number | 10-12 |

DOIs | |

State | Published - Jul 15 2008 |

### Keywords

- Analyticity
- Coriolis force
- Frequency set
- Navier-Stokes equations

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics

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## Cite this

Giga, Y., Jo, H., Mahalov, A., & Yoneda, T. (2008). On time analyticity of the Navier-Stokes equations in a rotating frame with spatially almost periodic data.

*Physica D: Nonlinear Phenomena*,*237*(10-12), 1422-1428. https://doi.org/10.1016/j.physd.2008.03.007