Enhanced dissipation by advection and applications to PDEs
Anna L. Mazzucato, Yuanyuan Feng, and Camilla Nobili
TL;DR
This survey explores how advection enhances dissipation in PDEs, covering physical principles, mathematical analysis, and applications to nonlinear equations like Cahn-Hilliard and Kuramoto-Sivashinsky.
Contribution
It provides a comprehensive overview of enhanced dissipation phenomena, linking physical intuition with rigorous mathematical results and applications in nonlinear PDEs.
Findings
Key mechanisms of enhanced dissipation identified
Mathematical formulations of advection-diffusion interactions
Applications to nonlinear PDEs like Cahn-Hilliard and Kuramoto-Sivashinsky
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsFluid Dynamics and Turbulent Flows · Heat Transfer and Boiling Studies · Heat Transfer and Optimization