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Random walks, random flows, and enhanced diffusivity in advection-diffusion equations

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  • We study the phenomenon of enhanced diffusivity, introduced by G. I.Taylor, for a class of advection-diffusion equations, modeling, for example, the spread of an ink drop in a fluid engaged in Poiseuille flow. We consider such flow in a pipe of general cross section, and compute variances and covariances of certain random flows associated with the advection-diffusion. We examine both long time behavior, including a central limit theorem, and short time asymptotics.
    Mathematics Subject Classification: Primary: 35K20, 35Q30; Secondary: 60J60.


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