Exponentially mixing flows with slow enhanced dissipation
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912510540513280 |
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| author | Cooperman, William Iyer, Gautam Rowan, Keefer Son, Seungjae |
| author_facet | Cooperman, William Iyer, Gautam Rowan, Keefer Son, Seungjae |
| contents | Consider a passive scalar which is advected by an incompressible flow $u$ and has small molecular diffusivity $κ$. Previous results show that if $u$ is exponentially mixing and $C^1$, then the dissipation time is $O(|\log κ|^2)$. We produce a family of incompressible flows which are $C^0$ and exponentially mixing, uniformly in $κ$; however have a dissipation time of order $1/κ$ (i.e. exhibits no enhanced dissipation). We also estimate the dissipation time of mixing flows, and obtain improved bounds in terms of the mixing rate with explicit constants, and allow for a time inhomogeneous mixing rate which is typical for random constructions of mixing flows. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_21305 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exponentially mixing flows with slow enhanced dissipation Cooperman, William Iyer, Gautam Rowan, Keefer Son, Seungjae Probability Analysis of PDEs Dynamical Systems 60J25, 35Q49, 76R05 Consider a passive scalar which is advected by an incompressible flow $u$ and has small molecular diffusivity $κ$. Previous results show that if $u$ is exponentially mixing and $C^1$, then the dissipation time is $O(|\log κ|^2)$. We produce a family of incompressible flows which are $C^0$ and exponentially mixing, uniformly in $κ$; however have a dissipation time of order $1/κ$ (i.e. exhibits no enhanced dissipation). We also estimate the dissipation time of mixing flows, and obtain improved bounds in terms of the mixing rate with explicit constants, and allow for a time inhomogeneous mixing rate which is typical for random constructions of mixing flows. |
| title | Exponentially mixing flows with slow enhanced dissipation |
| topic | Probability Analysis of PDEs Dynamical Systems 60J25, 35Q49, 76R05 |
| url | https://arxiv.org/abs/2507.21305 |