2D Euler equations with Stratonovich transport noise as a large scale stochastic model reduction

Abstract

The limit from an Euler type system to the 2D Euler equations with Stratonovich transport noise is investigated. A weak convergence result for the vorticity field and a strong convergence result for the velocity field are proved. Our results aim to provide a stochastic reduction of fluid-dynamics models with three different time scales.

arXiv comment30 pages

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• Quantitative mixing and dissipation enhancement property of Ornstein-Uhlenbeck flow
• 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
• Stochastic model reduction: convergence and applications to climate equations
• Finite time mixing and enhanced dissipation for 2D Navier--Stokes equations by Ornstein--Uhlenbeck flow