Finite time mixing and enhanced dissipation for 2D Navier--Stokes equations by Ornstein--Uhlenbeck flow
arXiv:2307.01493 · doi:10.1088/1361-6544/ada50f
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.
We have improved Theorem 1.2 by showing enhanced dissipation for all t>0