Gibbsian dynamics and ergodicity for the stochastically forced Navier-Stokes equation

E. Weinan; J. C. Mattingly; Ya Sinai

doi:10.1007/s002201224083

Gibbsian dynamics and ergodicity for the stochastically forced Navier-Stokes equation

E. Weinan, J. C. Mattingly, Ya Sinai

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Abstract

We study stationary measures for the two-dimensional Navier-Stokes equation with periodic boundary condition and random forcing. We prove uniqueness of the stationary measure under the condition that all "determining modes" are forced. The main idea behind the proof is to study the Gibbsian dynamics of the low modes obtained by representing the high modes as functionals of the time-history of the low modes.

Original language	English (US)
Pages (from-to)	83-106
Number of pages	24
Journal	Communications In Mathematical Physics
Volume	224
Issue number	1
DOIs	https://doi.org/10.1007/s002201224083
State	Published - 2001

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s002201224083

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abstract = "We study stationary measures for the two-dimensional Navier-Stokes equation with periodic boundary condition and random forcing. We prove uniqueness of the stationary measure under the condition that all {"}determining modes{"} are forced. The main idea behind the proof is to study the Gibbsian dynamics of the low modes obtained by representing the high modes as functionals of the time-history of the low modes.",

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AU - Mattingly, J. C.

AU - Sinai, Ya

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N2 - We study stationary measures for the two-dimensional Navier-Stokes equation with periodic boundary condition and random forcing. We prove uniqueness of the stationary measure under the condition that all "determining modes" are forced. The main idea behind the proof is to study the Gibbsian dynamics of the low modes obtained by representing the high modes as functionals of the time-history of the low modes.

AB - We study stationary measures for the two-dimensional Navier-Stokes equation with periodic boundary condition and random forcing. We prove uniqueness of the stationary measure under the condition that all "determining modes" are forced. The main idea behind the proof is to study the Gibbsian dynamics of the low modes obtained by representing the high modes as functionals of the time-history of the low modes.

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DO - 10.1007/s002201224083

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JO - Communications In Mathematical Physics

JF - Communications In Mathematical Physics

IS - 1

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Gibbsian dynamics and ergodicity for the stochastically forced Navier-Stokes equation

Abstract

All Science Journal Classification (ASJC) codes

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