Stochastic 3D Navier-Stokes equations in a thin domain and its α -approximation

Igor Chueshov; Sergei Kuksin

doi:10.1016/j.physd.2008.03.012

Stochastic 3D Navier-Stokes equations in a thin domain and its α -approximation

Igor Chueshov, Sergei Kuksin

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27 Citations (Scopus)

Abstract

In the thin domain O_e = T² × (0, e), where T² is a two-dimensional torus, we consider the 3D Navier-Stokes equations, perturbed by a white in time random force, and the Leray a-approximation for this system. We study ergodic properties of these models and their connection with the corresponding 2D models in the limit e ? 0. In particular, under natural conditions concerning the noise we show that in some rigorous sense the 2D stationary measure µ comprises asymptotical in time statistical properties of solutions for the 3D Navier-Stokes equations in O_e, when e « 1. © 2008 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	1352-1367
Number of pages	16
Journal	Physica D: Nonlinear Phenomena
Volume	237
Issue number	10-12
DOIs	https://doi.org/10.1016/j.physd.2008.03.012
Publication status	Published - 15 Jul 2008

Keywords

3D Navier-Stokes equations
Ergodicity
Leray α-model
Stationary measure
Thin domains
White noise

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10.1016/j.physd.2008.03.012

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title = "Stochastic 3D Navier-Stokes equations in a thin domain and its α -approximation",

abstract = "In the thin domain Oe = T2 × (0, e), where T2 is a two-dimensional torus, we consider the 3D Navier-Stokes equations, perturbed by a white in time random force, and the Leray a-approximation for this system. We study ergodic properties of these models and their connection with the corresponding 2D models in the limit e ? 0. In particular, under natural conditions concerning the noise we show that in some rigorous sense the 2D stationary measure µ comprises asymptotical in time statistical properties of solutions for the 3D Navier-Stokes equations in Oe, when e « 1. {\textcopyright} 2008 Elsevier B.V. All rights reserved.",

keywords = "3D Navier-Stokes equations, Ergodicity, Leray α-model, Stationary measure, Thin domains, White noise",

author = "Igor Chueshov and Sergei Kuksin",

year = "2008",

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doi = "10.1016/j.physd.2008.03.012",

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T1 - Stochastic 3D Navier-Stokes equations in a thin domain and its α -approximation

AU - Chueshov, Igor

AU - Kuksin, Sergei

PY - 2008/7/15

Y1 - 2008/7/15

N2 - In the thin domain Oe = T2 × (0, e), where T2 is a two-dimensional torus, we consider the 3D Navier-Stokes equations, perturbed by a white in time random force, and the Leray a-approximation for this system. We study ergodic properties of these models and their connection with the corresponding 2D models in the limit e ? 0. In particular, under natural conditions concerning the noise we show that in some rigorous sense the 2D stationary measure µ comprises asymptotical in time statistical properties of solutions for the 3D Navier-Stokes equations in Oe, when e « 1. © 2008 Elsevier B.V. All rights reserved.

AB - In the thin domain Oe = T2 × (0, e), where T2 is a two-dimensional torus, we consider the 3D Navier-Stokes equations, perturbed by a white in time random force, and the Leray a-approximation for this system. We study ergodic properties of these models and their connection with the corresponding 2D models in the limit e ? 0. In particular, under natural conditions concerning the noise we show that in some rigorous sense the 2D stationary measure µ comprises asymptotical in time statistical properties of solutions for the 3D Navier-Stokes equations in Oe, when e « 1. © 2008 Elsevier B.V. All rights reserved.

KW - 3D Navier-Stokes equations

KW - Ergodicity

KW - Leray α-model

KW - Stationary measure

KW - Thin domains

KW - White noise

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U2 - 10.1016/j.physd.2008.03.012

DO - 10.1016/j.physd.2008.03.012

M3 - Article

SN - 0167-2789

VL - 237

SP - 1352

EP - 1367

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

IS - 10-12

ER -

Stochastic 3D Navier-Stokes equations in a thin domain and its α -approximation

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