## Abstract

We consider solutions to the incompressible Navier-Stokes equations on the periodic domain Ω = [0, 2 π]^{3} with potential body forces. Let R ⊆ H^{1} (Ω)^{3} denote the set of all initial data that lead to regular solutions. Our main result is to construct a suitable Banach space S_{A}^{{star operator}} such that the normalization map W : R → S_{A}^{{star operator}} is continuous, and such that the normal form of the Navier-Stokes equations is a well-posed system in all of S_{A}^{{star operator}}. We also show that S_{A}^{{star operator}} may be seen as a subset of a larger Banach space V^{{star operator}} and that the extended Navier-Stokes equations, which are known to have global solutions, are well-posed in V^{{star operator}}.

Original language | English |
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Pages (from-to) | 1635-1673 |

Number of pages | 39 |

Journal | Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire |

Volume | 26 |

Issue number | 5 |

DOIs | |

State | Published - 2009 |

## Keywords

- Asymptotic expansion
- Long time dynamics
- Navier-Stokes equations
- Normal form
- Normalization map