Finite time mixing and enhanced dissipation for 2D Navier--Stokes equations by Ornstein--Uhlenbeck flow

TL;DR

This paper studies how a specific Ornstein-Uhlenbeck flow influences the mixing and dissipation properties of the 2D Navier-Stokes equations in a pathwise framework, revealing enhanced dissipation effects.

Contribution

It introduces a pathwise analysis of 2D Navier-Stokes equations perturbed by Ornstein-Uhlenbeck flow, demonstrating mixing and enhanced dissipation effects.

Findings

Proves mixing properties for the perturbed equations

Shows enhanced dissipation under certain flow conditions

Provides a pathwise interpretation contrasting previous stochastic approaches

Abstract

We consider the vorticity form of 2D Navier--Stokes equations perturbed by an Ornstein--Uhlenbeck flow of transport type. Contrary to previous works where the random perturbation was interpreted as Stratonovich transport noise, here we understand the equation in a pathwise manner and show the properties of mixing and enhanced dissipation for suitable choice of the flow.