Analysis of equilibrium states of Markov solutions to the 3D Navier-Stokes equations driven by additive noise

被引：20

作者：

Romito, Marco ^{[1
]}

机构：

[1] Univ Florence, Dipartimento Matemat, I-50134 Florence, Italy

来源：

JOURNAL OF STATISTICAL PHYSICS | 2008年 / 131卷 / 03期

关键词：

stochastic Navier-Stokes equations; martingale problem; Markov selections; invariant measures; ergodicity; energy balance;

D O I：

10.1007/s10955-007-9477-8

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We prove that every Markov solution to the three dimensional Navier-Stokes equations with periodic boundary conditions driven by additive Gaussian noise is uniquely ergodic. The convergence to the (unique) invariant measure is exponentially fast. Moreover, we give a well-posedness criterion for the equations in terms of invariant measures. We also analyse the energy balance and identify the term which ensures equality in the balance.

引用

页码：415 / 444

页数：30

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