Microscopic expression of anomalous dissipation in Passive scalar transport

TL;DR

This paper investigates the microscopic mechanisms behind anomalous dissipation in passive scalar transport, linking macroscopic energy loss to microscopic advection through kinetic theory analysis.

Contribution

It introduces a microscopic perspective on anomalous dissipation, connecting weak solutions of transport equations to kinetic theory insights.

Findings

Energy loss is associated with non-vanishing microscopic advection.

Provides a kinetic theory framework to understand anomalous dissipation.

Clarifies the microscopic properties of solutions with anomalous dissipation.

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.