### Abstract

We use the balance relations for the stationary in time solutions of the randomly forced 2D Navier-Stokes equations, found in [10], to study these solutions further. We show that the vorticity ?(t,x) of a stationary solution has a finite exponential moment, and that for any a ? R, t=0 the expectation of the integral of |d_{x}?| over the level-set {x|?(t,x)=a}, up to a constant factor equals the expectation of the integral of |d_{x}?| over the same set. © 2006 Springer Science + Business Media, Inc.

Original language | English |
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Pages (from-to) | 101-114 |

Number of pages | 14 |

Journal | Journal of Statistical Physics |

Volume | 122 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 2006 |

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### Keywords

- Balance relations
- Exponential moment
- Stationary measure
- Two-dimensional Navier-Stokes equation
- Vorticity

### Cite this

*Journal of Statistical Physics*,

*122*(1), 101-114. https://doi.org/10.1007/s10955-005-8084-9

}

*Journal of Statistical Physics*, vol. 122, no. 1, pp. 101-114. https://doi.org/10.1007/s10955-005-8084-9

**Remarks on the balance relations for the two-dimensional navier-stokes equation with random forcing.** / Kuksin, Sergei B.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Remarks on the balance relations for the two-dimensional navier-stokes equation with random forcing

AU - Kuksin, Sergei B.

PY - 2006/1

Y1 - 2006/1

N2 - We use the balance relations for the stationary in time solutions of the randomly forced 2D Navier-Stokes equations, found in [10], to study these solutions further. We show that the vorticity ?(t,x) of a stationary solution has a finite exponential moment, and that for any a ? R, t=0 the expectation of the integral of |dx?| over the level-set {x|?(t,x)=a}, up to a constant factor equals the expectation of the integral of |dx?| over the same set. © 2006 Springer Science + Business Media, Inc.

AB - We use the balance relations for the stationary in time solutions of the randomly forced 2D Navier-Stokes equations, found in [10], to study these solutions further. We show that the vorticity ?(t,x) of a stationary solution has a finite exponential moment, and that for any a ? R, t=0 the expectation of the integral of |dx?| over the level-set {x|?(t,x)=a}, up to a constant factor equals the expectation of the integral of |dx?| over the same set. © 2006 Springer Science + Business Media, Inc.

KW - Balance relations

KW - Exponential moment

KW - Stationary measure

KW - Two-dimensional Navier-Stokes equation

KW - Vorticity

UR - http://www.scopus.com/inward/record.url?scp=33644586027&partnerID=8YFLogxK

U2 - 10.1007/s10955-005-8084-9

DO - 10.1007/s10955-005-8084-9

M3 - Article

VL - 122

SP - 101

EP - 114

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 1

ER -