A dyadic model on a tree

Abstract

We study an infinite system of non-linear differential equations coupled in a tree-like structure. This system was previously introduced in the literature and it is the model from which the dyadic shell model of turbulence was derived. It mimics 3d Euler and Navier-Stokes equations in a rough approximation of a wavelet decomposition. We prove existence of finite energy solutions, anomalous dissipation in the inviscid unforced case, existence and uniqueness of stationary solutions (either conservative or not) in the forced case.

References in corpus (2)

• An inviscid dyadic model of turbulence: the fixed point and Onsager's conjecture
• The vanishing viscosity limit for a dyadic model

Cited by in corpus (10)

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• Stochastic Navier-Stokes Equations and Related Models
• Uniqueness for an inviscid stochastic dyadic model on a tree
• How close are shell models to the 3D Navier-Stokes equations?
• Well posedness and limit theorems for a class of stochastic dyadic models
• Structure function and fractal dissipation for an intermittent inviscid dyadic model
• Stochastic inviscid shell models: well-posedness and anomalous dissipation
• Regularized vortex approximation for 2D Euler equations with transport noise
• Linear Stochastic Dyadic model
• Dynamical Fractional and Multifractal Fields