Uniqueness of the Leray-Hopf solution for a dyadic model

TL;DR

This paper proves the uniqueness of Leray-Hopf solutions for a specific dyadic model of fluid dynamics, contributing to the mathematical understanding of such models.

Contribution

It establishes the uniqueness of Leray-Hopf solutions for a particular dyadic equation with smooth initial data, advancing theoretical knowledge.

Findings

Uniqueness of Leray-Hopf solutions is proven for the model.

The result applies to smooth initial data.

The paper clarifies the mathematical properties of the dyadic model.

Abstract

The dyadic problem $\dot u_n + \lambda^{2n} u_n - \lambda^{\beta n} u_{n-1}^2 + \lambda^{\beta(n+1)} u_n u_{n+1} = 0$ with "smooth" initial data is considered. The uniqueness of the Leray-Hopf solution is proved.