Well Posedness for Positive Dyadic Model

TL;DR

This paper proves the global existence and uniqueness of solutions for a positive dyadic model of Euler equations, extending results to a broad class of initial conditions in l^2.

Contribution

It establishes well-posedness for a dyadic Euler model, including global solutions for positive initial data in a large function space.

Findings

Global existence and uniqueness of solutions in class K

Solutions exist for all positive initial conditions in l^2

Results apply to a broad class of initial data

Abstract

We consider the solutions of the Cauchy problem for a dyadic model of Euler equations. We prove global existence and uniqueness of Leray-Hopf solutions in a rather large class K that implies in particular global existence and uniqueness in l^2 for all initial positive conditions in l^2.