EXPONENTIAL MIXING FOR RANDOM DYNAMICAL SYSTEMS AND AN EXAMPLE OF PIERREHUMBERT

• 成果类型: Article
• 署名作者: Blumenthal, Alex; Zelati, Michele Coti; Gvalani, Rishabh S.
• 署名单位: University System of Georgia; Georgia Institute of Technology; Imperial College London; Max Planck Society
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/23-AOP1627
• 发表日期: 2023
• 页码: 1559-1601
• 关键词: lyapunov exponents; lagrangian chaos; passive scalars; diffusion; advection; THEOREM; GROWTH; sample; rates; decay

摘要

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.