A universal total anomalous dissipator
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913671338262528 |
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| author | Hess-Childs, Elias Rowan, Keefer |
| author_facet | Hess-Childs, Elias Rowan, Keefer |
| contents | For all $α\in(0,1)$, we construct an explicit divergence-free vector field $V\in L^\infty_tC^α_x \cap C^{\fracα{1-α}}_t L^\infty_x$ so that the solutions to the drift-diffusion equations $$\partial_tθ^κ-κΔθ^κ+V\cdot\nablaθ^κ=0$$ exhibit asymptotic total dissipation for all mean-zero initial data: $\lim_{κ\rightarrow 0}\|θ^κ(1,\cdot)\|_{L^2}=0$. Additionally, we give explicit rates in $κ$ and uniform dependence on initial data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18526 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A universal total anomalous dissipator Hess-Childs, Elias Rowan, Keefer Analysis of PDEs Probability For all $α\in(0,1)$, we construct an explicit divergence-free vector field $V\in L^\infty_tC^α_x \cap C^{\fracα{1-α}}_t L^\infty_x$ so that the solutions to the drift-diffusion equations $$\partial_tθ^κ-κΔθ^κ+V\cdot\nablaθ^κ=0$$ exhibit asymptotic total dissipation for all mean-zero initial data: $\lim_{κ\rightarrow 0}\|θ^κ(1,\cdot)\|_{L^2}=0$. Additionally, we give explicit rates in $κ$ and uniform dependence on initial data. |
| title | A universal total anomalous dissipator |
| topic | Analysis of PDEs Probability |
| url | https://arxiv.org/abs/2501.18526 |