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

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.

arXiv commentWe have improved Theorem 1.2 by showing enhanced dissipation for all t>0

References in corpus (12)

• Well-posedness of the transport equation by stochastic perturbation
• Variational Principles for Stochastic Fluid Dynamics
• High mode transport noise improves vorticity blow-up control in 3D Navier-Stokes equations
• Almost-sure enhanced dissipation and uniform-in-diffusivity exponential mixing for advection-diffusion by stochastic Navier-Stokes
• 2D Euler equations with Stratonovich transport noise as a large scale stochastic model reduction
• From additive to transport noise in 2D fluid dynamics
• Quantitative convergence rates for scaling limit of SPDEs with transport noise
• Dissipation properties of transport noise in the two-layer quasi-geostrophic model
• Second order perturbation theory of two-scale systems in fluid dynamics
• Quantitative mixing and dissipation enhancement property of Ornstein-Uhlenbeck flow
• Enhanced dissipation for stochastic Navier-Stokes equations with transport noise
• Stabilization by transport noise and enhanced dissipation in the Kraichnan model