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arXiv · 2504.14564

Quenched correlation decay for random splittings of some prototypical 3D flows including the ABC flow

Nianci Jiang·Weili Zhang
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Abstract

For the long-time dynamical challenges of some prototypical 3D flows including the ABC flow on $\mathbb{T}^3$, we apply a random splitting method to establish two fundamental indicators of chaotic dynamics. First, under general assumptions, we establish that these random splittings exhibit Lagrangian chaos, characterized by a positive top Lyapunov exponent. Furthermore, we demonstrate the almost-sure quenched correlation decay of these random splittings, which is a stronger property than the almost-sure positivity of Lyapunov exponents alone. This framework is then applied to construct ideal dynamo in kinematic dynamo theory and to establish exponential mixing of passive scalars.

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Nianci Jiang, Weili Zhang. 2025-04-20. Quenched correlation decay for random splittings of some prototypical 3D flows including the ABC flow. https://arxiv.org/abs/2504.14564

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