Well posedness and limit theorems for a class of stochastic dyadic models
arXiv:2207.09631 · doi:10.1137/22M1511497
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.
arXiv comment35 pages
References in corpus (9)
- An optimal shell model of turbulence
- High mode transport noise improves vorticity blow-up control in 3D Navier-Stokes equations
- Eddy heat exchange at the boundary under white noise turbulence
- Stochastic Navier-Stokes Equations and Related Models
- Uniqueness for an inviscid stochastic dyadic model on a tree
- Anomalous dissipation in a stochastic inviscid dyadic model
- A dyadic model on a tree
- Regularization by transport noise for 3D MHD equations
- Structure function and fractal dissipation for an intermittent inviscid dyadic model