Linear Stochastic Dyadic model

TL;DR

This paper studies a stochastic particle system related to turbulence models, establishing existence, uniqueness, regularity, and invariant measures for a specific class of solutions called moderate solutions.

Contribution

It introduces a new stochastic dyadic model of turbulence, proving existence, uniqueness, and regularity results for moderate solutions, along with invariant measures.

Findings

Existence and uniqueness of solutions for the stochastic dyadic model.

Regularity properties of moderate solutions.

Existence and uniqueness of invariant measures.

Abstract

We discuss a stochastic interacting particles' system connected to dyadic models of turbulence, defining suitable classes of solutions and proving their existence and uniqueness. We investigate the regularity of a particular family of solutions, called moderate, and we conclude with existence and uniqueness of invariant measures associated with such moderate solutions.