Quantitative mixing and dissipation enhancement property of Ornstein-Uhlenbeck flow

TL;DR

This paper investigates how an Ornstein-Uhlenbeck flow enhances mixing and dissipation in solutions to the advection-diffusion equation, providing quantitative results uniform in diffusion and demonstrating finite-time dissipation enhancement.

Contribution

It offers a new quantitative analysis of mixing and dissipation enhancement under Ornstein-Uhlenbeck flows, with results uniform across diffusion parameters.

Findings

Proved a uniform quantitative mixing result.

Established finite-time dissipation enhancement.

Demonstrated the flow's effectiveness in mixing and dissipation.

Abstract

This work deals with mixing and dissipation ehancement for the solution of advection-diffusion equation driven by a Ornstein-Uhlenbeck velocity field. We are able to prove a quantitative mixing result, uniform in the diffusion parameter, and enhancement of dissipation over a finite time horizon.