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Enhanced dissipation by advection and applications to PDEs

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arxiv 2501.17695 v2 pith:LLLIMMFQ submitted 2025-01-29 math.AP math-phmath.MP

Anna L. Mazzucato , Yuanyuan Feng , Camilla Nobili This is my paper · ORCID
classification math.APmath-phmath.MP
keywords dissipationenhancedadvectionapplicationspdesanalysisbeginscahn-hilliard
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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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Cited by 1 Pith paper

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  1. Enhanced Dissipation via time-modulated velocity fields

    math.AP 2025-01 conditional novelty 6.0 of 10

    For time-modulated shear flows, the paper derives L2 decay estimates whose rates depend explicitly on the modulation, including faster-than-autonomous decay for growing flows and autonomous-like rates for slowly switc...

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