Enhanced dissipation by advection and applications to PDEs

A. L. Mazzucato; Y. Feng; C. Nobili

doi:10.1016/j.apm.2025.116310

Enhanced dissipation by advection and applications to PDEs

A. L. Mazzucato^*
, Y. Feng
, C. Nobili

^*Corresponding author for this work

School of Mathematical Sciences

Pennsylvania State University
University of Surrey

Research output: Contribution to journal › Article › peer-review

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 the Kuramoto-Sivashinsky equations.

Original language	English
Article number	116310
Journal	Applied Mathematical Modelling
Volume	150
DOIs	https://doi.org/10.1016/j.apm.2025.116310
State	Published - Feb 2026

Keywords

Advection
Enhanced dissipation
Hypocoercivity
Nonlinear PDEs
Resolvent estimate
Taylor's dispersion

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10.1016/j.apm.2025.116310

Cite this

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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 the Kuramoto-Sivashinsky equations.",

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N2 - 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 the Kuramoto-Sivashinsky equations.

AB - 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 the Kuramoto-Sivashinsky equations.

KW - Advection

KW - Enhanced dissipation

KW - Hypocoercivity

KW - Nonlinear PDEs

KW - Resolvent estimate

KW - Taylor's dispersion

UR - https://www.scopus.com/pages/publications/105011385793

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DO - 10.1016/j.apm.2025.116310

M3 - 文章

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JF - Applied Mathematical Modelling

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ER -

Enhanced dissipation by advection and applications to PDEs

Abstract

Keywords

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