Blowup of Dyadic MHD Models with Forward Energy Cascade

Abstract

Abstract A particular type of dyadic model for the magnetohydrodynamics (MHD) with dominating 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 or the dyadic Hall MHD model develops blowup in finite time. Moreover, for a class of positive initial data with large velocity components and small magnetic field components, we prove that there exists a positive solution that blows up at a finite time.