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

被引：142

作者：

Weinan E. ^{[1
,2
]}

Mattingly J.C. ^{[3
]}

Sinai Y. ^{[4
,5
]}

机构：

[1] Dept. of Math./Prog. in Appl./C., Princeton University, Princeton

[2] School of Mathematics, Peking University, Beijing

[3] Department of Mathematics, Stanford University, Stanford

[4] Department of Mathematics, Princeton University, Princeton

[5] Landau Inst. of Theoretical Physics, Moscow

来源：

Communications in Mathematical Physics | 2001年 / 224卷 / 1期

关键词：

D O I：

10.1007/s002201224083

中图分类号：

学科分类号：

摘要：

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.

引用

页码：83 / 106

页数：23

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