### Abstract

We prove existence of global regular solutions for the 3D Navier-Stokes equations with (or without) Coriolis force for a class of initial data u_{0} in the space FM_{σ,δ}, i.e., for functions whose Fourier image û_{0} is a vector-valued Radon measure and that are supported in sumclosed frequency sets with distance δ from the origin. In our main result we establish an upper bound for admissible initial data in terms of the Reynolds number, uniform on the Coriolis parameter ω. In particular this means that this upper bound is linearly growing in δ. This implies that we obtain global-in-time regular solutions for large (in norm) initial data u_{0} which may not decay at space infinity, provided that the distance δ of the sum-closed frequency set from the origin is sufficiently large.

Original language | English (US) |
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Pages (from-to) | 721-736 |

Number of pages | 16 |

Journal | Advances in Differential Equations |

Volume | 12 |

Issue number | 7 |

State | Published - Dec 1 2007 |

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

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## Cite this

*Advances in Differential Equations*,

*12*(7), 721-736.