Duke Applied Mathematics

Publications [#383624] 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 T2, Duke Mathematical Journal, vol. 174 no. 7 (May, 2025), pp. 1209-1260 [doi]
   (last updated on 2026/01/19)

   Abstract:
   We consider the advection-diffusion equation on T² with a Lipschitz and time-periodic velocity field that alternates between two piecewise linear shear flows. We prove enhanced dissipation on the timescale |log υ|, where υ is the diffusivity parameter. This is the optimal decay rate as υ → 0 for uniformly-in-time Lipschitz velocity fields. We also establish exponential mixing for the υ = 0 problem.