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arXiv · 2305.08090

Anomalous and total dissipation due to advection by solutions of randomly forced Navier-Stokes equations

Martina Hofmanová·Umberto Pappalettera·Rongchan Zhu·Xiangchan Zhu
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Abstract

We propose a novel approach to induce anomalous dissipation through advection driven by turbulent fluid flows. Specifically, we establish the existence of a velocity field $v$ satisfying randomly forced Navier-Stokes equations, leading to total dissipation of kinetic energy in finite time when advecting a passive scalar. This dissipation phenomenon is uniform across viscosity parameters and initial conditions, representing a case of anomalous dissipation. We further explore dissipation induced by individual realizations of $v$. Our results extend to scenarios where the passive scalar is replaced by solutions to two or three-dimensional deterministic Navier-Stokes equations advected by $v$.

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Martina Hofmanová, Umberto Pappalettera, Rongchan Zhu, Xiangchan Zhu. 2023-05-14. Anomalous and total dissipation due to advection by solutions of randomly forced Navier-Stokes equations. https://arxiv.org/abs/2305.08090

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