A stationary solution for the mixed turbulence shell model

TL;DR

This paper proves the existence of stationary solutions for the mixed turbulence shell model under Gaussian initial conditions, extending previous results to a broader class of initial states and related turbulence models.

Contribution

It extends classic existence results from bcl^2 to bcmu-almost every initial condition for the mixed shell model and similar turbulence models with a dyadic tree structure.

Findings

Existence of stationary solutions for the mixed shell model.

Extension of results to bcmu-almost every initial condition.

Applicability to turbulence models with dyadic tree structure.

Abstract

The aim of this work is to prove an existence result on the mixed shell model extending the classic standard existence results from $\ell^2$ initial conditions to $\mu$-almost every initial conditions, where $\mu$ is a Gaussian measure on the infinite dimensional space of initial conditions. A similar result is also shown to hold for turbulence models where a dyadic tree structure replaces the linear one.