Ergodic properties of highly degenerate 2D stochastic Navier-Stokes equations

被引：12

作者：

Hairer, M ^{[1
]}

Mattingly, JC

机构：

[1] Univ Warwick, Dept Math, Coventry CV4 7AL, W Midlands, England

[2] Duke Univ, Dept Math, Durham, NC 27708 USA

来源：

COMPTES RENDUS MATHEMATIQUE | 2004年 / 339卷 / 12期

关键词：

D O I：

10.1016/j.crma.2004.09.035

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This Note presents the results from "Ergodicity of the degenerate stochastic 2D Navier-Stokes equation" by M. Hairer and J.C. Mattingly. We study the Navier-Stokes equation on the two-dimensional torus when forced by a finite dimensional Gaussian white noise and give conditions under which the system is ergodic. In particular, our results hold for specific choices of four-dimensional Gaussian white noise. (C) 2004 Academie des sciences. Published by Elsevier SAS. All rights reserved.

引用

页码：879 / 882

页数：4

共 19 条

[1] Exponential mixing of the 2D stochastic Navier-Stokes dynamics [J].

Bricmont, J ;

Kupiainen, A ;

Lefevere, R .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2002, 230 (01) :87-132

[2] Ergodicity of the 2D Navier-Stokes equations with random forcing [J].

Bricmont, J ;

Kupiainen, A ;

Lefevere, R .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2001, 224 (01) :65-81

[3]

CRUZEIRO AB, 1989, EXPO MATH, V7, P73

[4]

E WN, 2002, J STAT PHYS, V108, P1125

[5]

E WN, 2001, COMMUN PUR APPL MATH, V54, P1386

[6]

Ferrario B., 1997, STOCHASTICS STOCHAST, V60, P271

[7] ERGODICITY OF THE 2-D NAVIER-STOKES EQUATION UNDER RANDOM PERTURBATIONS [J].

FLANDOLI, F ;

MASLOWSKI, B .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1995, 172 (01) :119-141

[8]

Flandoli F., 1994, NODEA-NONLINEAR DIFF, V1, P403

[9] Exponential mixing properties of stochastic PDEs through asymptotic coupling [J].

Hairer, M .

PROBABILITY THEORY AND RELATED FIELDS, 2002, 124 (03) :345-380

[10]

HAIRER M, 2004, UNPUB ERGODICITY DEG

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