Anomalous Dissipation at Onsager-Critical Regularity

Alexey Cheskidov; Qirui Peng

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arXiv · 2512.24568

Anomalous Dissipation at Onsager-Critical Regularity

Alexey Cheskidov·Qirui Peng

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Abstract

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}.

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Alexey Cheskidov, Qirui Peng. 2025-12-31. Anomalous Dissipation at Onsager-Critical Regularity. https://arxiv.org/abs/2512.24568

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