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Optimal enhanced dissipation and mixing for a time-periodic, Lipschitz velocity field on $\mathbb{T}^2$

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arxiv 2304.05374 v1 pith:3P73BPNT submitted 2023-04-11 math.AP math.DSmath.PR

Tarek M. Elgindi , Kyle Liss , Jonathan C. Mattingly This is my paper · ORCID
classification math.APmath.DSmath.PR
keywords lipschitzvelocitydissipationenhancedfieldmathbbmixingoptimal
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abstract

We consider the advection-diffusion equation on $\mathbb{T}^2$ with a Lipschitz and time-periodic velocity field that alternates between two piecewise linear shear flows. We prove enhanced dissipation on the timescale $|\log \nu|$, where $\nu$ is the diffusivity parameter. This is the optimal decay rate as $\nu \to 0$ for uniformly-in-time Lipschitz velocity fields. We also establish exponential mixing for the $\nu = 0$ problem.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Sampling and Optimization meet Enhanced Flows

    math.OC 2026-08 conditional novelty 7.0 of 10

    New first- and second-order transport-diffusion dynamics with deterministic alternating shear flows converge to a given Gibbs measure at an enhanced O(ν^{1/2}) rate, faster than classical Langevin sampling at O(ν).

  2. Turbulent and intermittent phenomena in a universal total anomalous dissipator

    math.AP 2025-07 unverdicted novelty 6.0 of 10

    An explicit incompressible flow on the 2-torus is constructed that simultaneously causes anomalous dissipation, Richardson dispersion, anomalous regularization, and spatial intermittency for every Hölder exponent below 1.

  3. 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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