Quenched correlation decay for random splittings of some prototypical 3D flows including the ABC flow
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912337753014272 |
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| author | Jiang, Nianci Zhang, Weili |
| author_facet | Jiang, Nianci Zhang, Weili |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_14564 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quenched correlation decay for random splittings of some prototypical 3D flows including the ABC flow Jiang, Nianci Zhang, Weili Dynamical Systems Probability 37A25, 37H05, 76W05, 76F25, 35Q49 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. |
| title | Quenched correlation decay for random splittings of some prototypical 3D flows including the ABC flow |
| topic | Dynamical Systems Probability 37A25, 37H05, 76W05, 76F25, 35Q49 |
| url | https://arxiv.org/abs/2504.14564 |