From additive to transport noise in 2D fluid dynamics

Abstract

Additive noise in Partial Differential equations, in particular those of fluid mechanics, has relatively natural motivations. The aim of this work is showing that suitable multiscale arguments lead rigorously, from a model of fluid with additive noise, to transport type noise. The arguments apply both to small-scale random perturbations of the fluid acting on a large-scale passive scalar and to the action of the former on the large scales of the fluid itself. Our approach consists in studying the (stochastic) characteristics associated to small-scale random perturbations of the fluid, here modelled by stochastic 2D Euler equations with additive noise, and their convergence in the infinite scale separation limit.

31 pages

References in corpus (5)

• Global L_2-solutions of stochastic Navier-Stokes equations
• 2D Euler equations with Stratonovich transport noise as a large scale stochastic model reduction
• Eddy heat exchange at the boundary under white noise turbulence
• Quantitative mixing and dissipation enhancement property of Ornstein-Uhlenbeck flow
• Well-Posedness of the 3D Stochastic Primitive Equations with Transport Noise

Cited by in corpus (6)

• Global existence and non-uniqueness of 3D Euler equations perturbed by transport noise
• Global existence and non-uniqueness for the Cauchy problem associated to 3D Navier-Stokes equations perturbed by transport noise
• Enhanced dissipation for stochastic Navier-Stokes equations with transport noise
• Quantitative mixing and dissipation enhancement property of Ornstein-Uhlenbeck flow
• Inviscid Limit for Stochastic Second-Grade Fluid Equations
• Finite time mixing and enhanced dissipation for 2D Navier--Stokes equations by Ornstein--Uhlenbeck flow