Duke Applied Mathematics

Publications [#370164] of Jonathan C. Mattingly

Papers Published

1. Elgindi, TM; Liss, K; Mattingly, JC, Optimal enhanced dissipation and mixing for a time-periodic, Lipschitz velocity field on $\mathbb{T}^2$ (April, 2023)
   (last updated on 2026/01/20)

   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.