Microscopic expression of anomalous dissipation in Passive scalar transport

2022/12/13 by Tomonori Tsuruhashi, Tsuruhashi, Tomonori, Tsuyoshi Yoneda +1 · 1 citation
Engineering · Mathematics · #35A02 #35D30 #35Q35 #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2212.06395

openalex publication_date 2022/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study anomalous dissipation from a microscopic viewpoint. In the work by Drivas, Elgindi, Iyer and Jeong (2022), the property of anomalous dissipation provides the existence of non-unique weak solutions for a transport equation with a singular velocity field. In this paper, we reconsider this solution in terms of kinetic theory and clarify its microscopic property. Consequently, energy loss can be expressed by non-vanishing microscopic advection.

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