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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.15001 |
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| _version_ | 1866917576120991744 |
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| author | Rowan, Keefer |
| author_facet | Rowan, Keefer |
| contents | We show that by "accelerating" relaxation enhancing flows, one can construct a flow that is smooth on $[0,1) \times \mathbb{T}^d$ but highly singular at $t=1$ so that for any positive diffusivity, the advection-diffusion equation associated to the accelerated flow totally dissipates solutions, taking arbitrary initial data to the constant function at $t=1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15001 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Accelerated relaxation enhancing flows cause total dissipation Rowan, Keefer Analysis of PDEs We show that by "accelerating" relaxation enhancing flows, one can construct a flow that is smooth on $[0,1) \times \mathbb{T}^d$ but highly singular at $t=1$ so that for any positive diffusivity, the advection-diffusion equation associated to the accelerated flow totally dissipates solutions, taking arbitrary initial data to the constant function at $t=1$. |
| title | Accelerated relaxation enhancing flows cause total dissipation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2401.15001 |