Well posedness and limit theorems for a class of stochastic dyadic models

Abstract

We consider stochastic inviscid dyadic models with energy-preserving noise. It is shown that the models admit weak solutions which are unique in law. Under a certain scaling limit of the noise, the stochastic models converge weakly to a deterministic viscous dyadic model, for which we provide explicit convergence rates in terms of the parameters of noise. A central limit theorem underlying such scaling limit is also established. In case that the stochastic dyadic model is viscous, we show the phenomenon of dissipation enhancement for suitably chosen noise.

35 pages

References in corpus (2)

• Eddy heat exchange at the boundary under white noise turbulence
• Regularization by transport noise for 3D MHD equations

Cited by in corpus (2)

• LDP and CLT for SPDEs with Transport Noise
• Enhanced dissipation for stochastic Navier-Stokes equations with transport noise