### Abstract

We consider the 2D Navier-Stokes system, perturbed by a random force, such that sufficiently many of its Fourier modes are excited (e.g. all of them are). We discuss the results on the existence and uniqueness of a stationary measure for this system, obtained in last years, homogeneity of the measures and some their limiting properties. Next we use these results to prove that solutions of the equations obey the central limit theorem and the strong law of large numbers.

Original language | English |
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Pages (from-to) | 585-600 |

Number of pages | 16 |

Journal | Reviews in Mathematical Physics |

Volume | 14 |

Issue number | 6 |

DOIs | |

Publication status | Published - Jun 2002 |

### Keywords

- Central limit theorem
- Homogeneous measure
- Navier-Stokes system
- Random force
- Stationary measure
- Strong law of large numbers

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## Cite this

Kuksin, S. B. (2002). Ergodic theorems for 2D statistical hydrodynamics.

*Reviews in Mathematical Physics*,*14*(6), 585-600. https://doi.org/10.1142/S0129055X02001338