### 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 |

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### Keywords

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

### Cite this

*Reviews in Mathematical Physics*,

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

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*Reviews in Mathematical Physics*, vol. 14, no. 6, pp. 585-600. https://doi.org/10.1142/S0129055X02001338

**Ergodic theorems for 2D statistical hydrodynamics.** / Kuksin, Sergei B.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Ergodic theorems for 2D statistical hydrodynamics

AU - Kuksin, Sergei B.

PY - 2002/6

Y1 - 2002/6

N2 - 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.

AB - 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.

KW - Central limit theorem

KW - Homogeneous measure

KW - Navier-Stokes system

KW - Random force

KW - Stationary measure

KW - Strong law of large numbers

UR - http://www.scopus.com/inward/record.url?scp=0036600055&partnerID=8YFLogxK

U2 - 10.1142/S0129055X02001338

DO - 10.1142/S0129055X02001338

M3 - Article

VL - 14

SP - 585

EP - 600

JO - Reviews in Mathematical Physics

JF - Reviews in Mathematical Physics

SN - 0129-055X

IS - 6

ER -