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

Sergei B. Kuksin

doi:10.1007/s10955-005-8084-9

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

Sergei B. Kuksin

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

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
Pages (from-to)	101-114
Number of pages	14
Journal	Journal of Statistical Physics
Volume	122
Issue number	1
DOIs	https://doi.org/10.1007/s10955-005-8084-9
Publication status	Published - Jan 2006

Keywords

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

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10.1007/s10955-005-8084-9

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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.

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KW - Stationary measure

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

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Keywords

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