Uniqueness and non-uniqueness results for dyadic MHD models

Abstract

We construct non-unique Leray-Hopf solutions for some dyadic models for magnetohydrodynamics when the intermittency dimension $\delta$ is less than 1. In contrast, uniqueness of Leray-Hopf solution is established in the case of $\delta\geq 1$. Analogous results on uniqueness and non-uniqueness of Leray-Hopf solution are also obtained for dyadic models of MHD with fractional diffusion.