Uniqueness of the Leray-Hopf solution for a dyadic model

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.