Blow-up of dyadic MHD models with forward energy cascade

Abstract

A particular type of dyadic model for the magnetohydrodynamics (MHD) with forward energy cascade is studied. The model includes intermittency dimension $\delta$ in the nonlinear scales. It is shown that when $\delta$ is small, positive solution with large initial data for either the dyadic MHD model or the dyadic Hall MHD develops blow-up in finite time.