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 switched flows.
Enhanced dissipation by advection and applications to PDEs
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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 Kuramoto-Sivashinsky equations.
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Enhanced Dissipation via time-modulated velocity fields
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 switched flows.