Superexponential dissipation enhancement on $\mathbb{T}^d$
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911133999300608 |
|---|---|
| author | Rowan, Keefer |
| author_facet | Rowan, Keefer |
| contents | We construct incompressible velocity fields that exhibit faster than exponential dissipation for particular solutions to the advection-diffusion equation on $\mathbb{T}^d$. In 2D, we construct a velocity field in $L^\infty_{t,x}$ and exhibit a solution that decays with double exponential rate $e^{-C^{-1} e^{C^{-1}t}}$. In 3D, we construct a velocity field in $L^\infty_t W^{1,\infty}_x$ and exhibit a solution that decays with rate $e^{-C^{-1} t^2}$. In 4D, we construct a velocity field in $L^\infty_t C^\infty_x$ and exhibit a solution that decays with *some* superexponential rate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_02081 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Superexponential dissipation enhancement on $\mathbb{T}^d$ Rowan, Keefer Analysis of PDEs We construct incompressible velocity fields that exhibit faster than exponential dissipation for particular solutions to the advection-diffusion equation on $\mathbb{T}^d$. In 2D, we construct a velocity field in $L^\infty_{t,x}$ and exhibit a solution that decays with double exponential rate $e^{-C^{-1} e^{C^{-1}t}}$. In 3D, we construct a velocity field in $L^\infty_t W^{1,\infty}_x$ and exhibit a solution that decays with rate $e^{-C^{-1} t^2}$. In 4D, we construct a velocity field in $L^\infty_t C^\infty_x$ and exhibit a solution that decays with *some* superexponential rate. |
| title | Superexponential dissipation enhancement on $\mathbb{T}^d$ |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.02081 |