论文标题
随机动态系统的指数混合和Pierrehumbert的一个例子
Exponential mixing for random dynamical systems and an example of Pierrehumbert
论文作者
论文摘要
我们考虑在没有边界的任意紧凑型歧管上随机动态系统的指数混合问题。我们提出了一个强大的，基于动态的框架，使我们能够构建时空平滑，在时间上均匀界定的通用指数混合器。然后将该框架应用于1994年Pierrehumbert提出的经典示例中证明指数混合的问题，该框架包括具有随机相的交替的周期性剪切流。这解决了一个长期的开放问题，以证明存在时空平滑（通用）指数式混合不可压缩速度场在二维周期性域上的存在，同时还提供了一个工具箱，用于在所有维度中构造这种平滑的通用混合器。
We consider the question of exponential mixing for random dynamical systems on arbitrary compact manifolds without boundary. We put forward a robust, dynamics-based framework that allows us to construct space-time smooth, uniformly bounded in time, universal exponential mixers. The framework is then applied to the problem of proving exponential mixing in a classical example proposed by Pierrehumbert in 1994, consisting of alternating periodic shear flows with randomized phases. This settles a longstanding open problem on proving the existence of a space-time smooth (universal) exponentially mixing incompressible velocity field on a two-dimensional periodic domain while also providing a toolbox for constructing such smooth universal mixers in all dimensions.
