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arXiv · 2310.02934

Anomalous dissipation and Euler flows

Jan Burczak·László Székelyhidi Jr.·Bian Wu
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Abstract

We show anomalous dissipation of scalars advected by weak solutions to the incompressible Euler equations with $C^{(\sfrac{1}{3})^-}$ regularity, for an arbitrary initial datum in $\dot H^1 (\T^3)$. This is the first rigorous derivation of zeroth law of scalar turbulence, where the scalar is advected by solution to an equation of hydrodynamics (unforced and deterministic). As a byproduct of our method, we provide a typicality statement for the drift, and recover certain desired properties of turbulence, including a lower bound on scalar variance commensurate with the Richardson pair dispersion hypothesis.

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Jan Burczak, László Székelyhidi Jr., Bian Wu. 2023-10-04. Anomalous dissipation and Euler flows. https://arxiv.org/abs/2310.02934

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