This paper continues our study of the interconnection between controllability and mixing properties of random dynamical systems. We begin with an abstract result showing that the approximate controllability to a point and a local stabilisation property imply the uniqueness of a stationary measure and exponential mixing in the dual-Lipschitz metric. This result is then applied to the 2D Navier-Stokes system driven by a random force acting through the boundary. A by-product of our analysis is the local exponential stabilisation of the boundary-driven Navier-Stokes system by a regular boundary control.

中文翻译：

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可控性意味着混合 II。双李普希茨度量的收敛

本文继续研究随机动力系统的可控性和混合特性之间的相互联系。我们从一个抽象结果开始，该结果表明对一个点的近似可控性和局部稳定特性意味着双利普希茨度量中的平稳测度和指数混合的唯一性。然后将此结果应用于由通过边界作用的随机力驱动的 2D Navier-Stokes 系统。我们分析的一个副产品是边界驱动的纳维-斯托克斯系统通过规则边界控制的局部指数稳定。