Anomalous Dissipation at Onsager-Critical Regularity
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911347555434496 |
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| author | Cheskidov, Alexey Peng, Qirui |
| author_facet | Cheskidov, Alexey Peng, Qirui |
| contents | We construct solutions to the three-dimensional Euler equations exhibiting anomalous dissipation in finite time through a vanishing viscosity limit. Inspired by \cite{BDL23} and \cite{cheskidov2023dissipation}, we extend the \(2\frac{1}{2}\)-dimensional constructions and establish an Onsager-critical energy criterion adapted to such flows, showing its sharpness. Moreover, we provide a fully three-dimensional dissipative Euler example, sharp in Onsager's sense, driven by a slightly rough external force, following the framework of \cite{CL21}. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_24568 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Anomalous Dissipation at Onsager-Critical Regularity Cheskidov, Alexey Peng, Qirui Analysis of PDEs We construct solutions to the three-dimensional Euler equations exhibiting anomalous dissipation in finite time through a vanishing viscosity limit. Inspired by \cite{BDL23} and \cite{cheskidov2023dissipation}, we extend the \(2\frac{1}{2}\)-dimensional constructions and establish an Onsager-critical energy criterion adapted to such flows, showing its sharpness. Moreover, we provide a fully three-dimensional dissipative Euler example, sharp in Onsager's sense, driven by a slightly rough external force, following the framework of \cite{CL21}. |
| title | Anomalous Dissipation at Onsager-Critical Regularity |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2512.24568 |