Optimality of Exponential Mixing Rates in the Diffusive Setting

Determine whether the exponential mixing rates achieved for diffusive stochastic fluid systems represent optimal mixing rates.

Background

The paper discusses the difficulty of identifying optimal mixing strategies in the advection-diffusion setting because absolute lower bounds on achievable mix-norm decay are not available. It notes that exponential mixing rates have been achieved for stochastic fluid systems with diffusion and that these rates agree closely with prior numerical observations. However, the optimality of those rates is not established, leaving unresolved whether any admissible stirring strategy can produce faster mixing.