Enhanced dissipation by advection and applications to PDEs
Analysis of PDEs
2025-02-03 v2 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.2501.17695,
title = {Enhanced dissipation by advection and applications to PDEs},
author = {Anna L. Mazzucato and Yuanyuan Feng and Camilla Nobili},
journal= {arXiv preprint arXiv:2501.17695},
year = {2025}
}
Comments
29 pages, 3 figures