Enhanced dissipation by advection and applications to PDEs

2025/01/29 by Anna L. Mazzucato, Yuanyuan Feng, Mazzucato, Anna L. +3
Engineering · #35Qxx 76F10 #76Rxx #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Heat Transfer and Boiling Studies #Heat Transfer and Optimization #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.2501.17695

openalex publication_date 2025/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This survey provides a concise yet comprehensive overview on enhanced dissipation phenomena, transitioning seamlessly from the physical principles underlying the interplay between advection and diffusion to their rigorous mathematical formulation and analysis. The discussion begins with the standard theory of enhanced dissipation, highlighting key mechanisms and results, and progresses to its applications in notable nonlinear PDEs such as the Cahn-Hilliard and Kuramoto-Sivashinsky equations.

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