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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.27331 |
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| _version_ | 1866917052702261248 |
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| author | Romito, Marco Roveri, Leonardo |
| author_facet | Romito, Marco Roveri, Leonardo |
| contents | This paper investigates enhanced dissipation for a passive scalar advected by "very rough" horizontal shear flows, described by an advection-diffusion equation on the 2D torus. The authors extend results of Galeati and Gubinelli (2023) to generic flows in negative Besov spaces, proving that the dissipation rate increases to infinity as viscosity vanishes. This is obtained by deriving (non-sharp) upper and lower bounds on the dissipation rate. The upper bound holds for truly irregular velocities, namely those verifying a suitable version of the Wei irregularity index (Wei (2021)). As a by-product, it follows that for truly rough shear flows the vanishing viscosity solution to the corresponding inviscid equation is trivial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_27331 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Instantaneous Total Enhanced Dissipation For Very Rough Shear Flows Romito, Marco Roveri, Leonardo Analysis of PDEs 76F25, 35Q35, 35R05 This paper investigates enhanced dissipation for a passive scalar advected by "very rough" horizontal shear flows, described by an advection-diffusion equation on the 2D torus. The authors extend results of Galeati and Gubinelli (2023) to generic flows in negative Besov spaces, proving that the dissipation rate increases to infinity as viscosity vanishes. This is obtained by deriving (non-sharp) upper and lower bounds on the dissipation rate. The upper bound holds for truly irregular velocities, namely those verifying a suitable version of the Wei irregularity index (Wei (2021)). As a by-product, it follows that for truly rough shear flows the vanishing viscosity solution to the corresponding inviscid equation is trivial. |
| title | Instantaneous Total Enhanced Dissipation For Very Rough Shear Flows |
| topic | Analysis of PDEs 76F25, 35Q35, 35R05 |
| url | https://arxiv.org/abs/2510.27331 |