Ergodicity of the 3D stochastic Navier-Stokes equations driven by mildly degenerate noise

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:121

Article

Romito, Marco¹  Xu, Lihu² 

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

[2] EURANDOM, NL-5600 MB Eindhoven, Netherlands

关键词: Stochastic Navier-Stokes equations;    Martingale problem;    Markov selections;    Continuous dependence;    Ergodicity;    Degenerate noise;    Malliavin calculus;   

DOI  :  10.1016/j.spa.2010.11.010

来源: Elsevier

【 摘 要 】

We prove that any Markov solution to the 3D stochastic Navier-Stokes equations driven by a mildly degenerate noise (i.e. all but finitely many Fourier modes are forced) is uniquely ergodic. This follows by proving strong Feller regularity and irreducibility. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free