Mixing in incompressible flows: transport, dissipation, and their interplay

TL;DR

This survey explores the mathematical analysis of mixing in incompressible flows, focusing on PDEs, optimal mixing, regularity loss, and dissipation phenomena relevant to fluid dynamics applications.

Contribution

It provides a comprehensive overview of recent advances in understanding mixing, dissipation, and regularity loss in incompressible fluid flows through PDE analysis.

Findings

Overview of optimal mixing strategies

Insights into loss of regularity in transport equations

Discussion of enhanced and anomalous dissipation phenomena

Abstract

In this survey, we address mixing from the point of view of partial differential equations, motivated by applications that arise in fluid dynamics. We give an account of optimal mixing, loss of regularity for transport equations, enhanced dissipation, and anomalous dissipation.