Exponential mixing of the 2D stochastic Navier-Stokes dynamics

被引：64
作者：
Bricmont, J [1 ]
Kupiainen, A
Lefevere, R
机构：
[1] Univ Catholique Louvain, B-1348 Louvain, Belgium
[2] Univ Helsinki, Dept Math, FIN-00014 Helsinki, Finland
来源：
COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2002年 / 230卷 / 01期
关键词：
D O I：
10.1007/s00220-002-0708-1
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We consider the Navier-Stokes equation on a two dimensional torus with a random force which is white noise in time, and excites only a finite number of modes. The number of excited modes depends on the viscosity v, and grows like v(-3) when v goes to zero. We prove that this Markov process has a unique invariant measure and is exponentially mixing in time.
引用
收藏
页码：87 / 132
页数：46
相关论文
共 10 条
[1]   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
[2]  
BRICMONT J, J STAT PHYS, V100, P743
[3]  
Doob J. L., 1953, Stochastic processes, V101
[4]  
FLANDOLI F, 1995, COMMUN MATH PHYS, V171, P119
[5]  
Frisch U., 1995, TURBULENCE, DOI [10.1017/CBO9781139170666, DOI 10.1017/CBO9781139170666]
[6]   Stochastic dissipative PDE's and Gibbs measures [J].
Kuksin, S ;
Shirikyan, A .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2000, 213 (02) :291-330
[7]   Ergodicity of 2D Navier-Stokes equations with random forcing and large viscosity [J].
Mattingly, JC .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1999, 206 (02) :273-288
[8]   Gibbsian dynamics and ergodicity for the stochastically forced Navier-Stokes equation [J].
Weinan E. ;
Mattingly J.C. ;
Sinai Y. .
Communications in Mathematical Physics, 2001, 224 (1) :83-106
[9]  
SIMON B., 1979, Functional Integration and Quantum Physics
[10]  
Vishik M. J., 1980, MATH PROBLEMS STAT H
1