## Abstract

In this paper we study the Fourier transform of the 3D -Navier-Stokes System without external forcing on the whole space R ^{3}. The properties of solutions depend very much on the space in which the system is considered. In this paper we deal with the space Φ (α , α ) of functions v(k ) = c(k)/|k|α where α = 2 + ε, ε > 0 and c (k) is bounded, sup_{k∈ R3\0}|c(k)< ∞ . We construct the power series which converges for small t and gives solutions of the system for bounded intervals of time. These solutions can be estimated at infinity (in k-space) by exp {-const√t|k|}.

Original language | English (US) |
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Pages (from-to) | 779-803 |

Number of pages | 25 |

Journal | Journal of Statistical Physics |

Volume | 121 |

Issue number | 5-6 |

DOIs | |

State | Published - Dec 2005 |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

## Keywords

- Fourier transform
- Navier-Stokes System
- Power series

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