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We derive dyadic models for the magnetohydrodynamics with Hall effect byincluding the intermittency dimension as a parameter. For such dyadic models,existence of global weak solutions is established. In addition, local strongsolution is obtained; while global strong solution is obtained in the case ofhigh intermittency dimension. Moreover, we show that positive solution withlarge initial data develops blow-up in finite time provided the intermittencydimension is lower than a threshold.

Dyadic models with intermittency dependence for the Hall MHD