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We consider here the magneto-hydrodynamics (MHD) equations on the wholespace. For the 3D case, in the setting of the weighted $L^2$ spaces we obtain aweak-strong uniqueness criterion provided that the velocity field and themagnetic field belong to a fairly general multipliers space. On the other hand,we study the local and global existence of weak suitable solutions forintermittent initial data, which is characterized through a local Morrey space.This large initial data space was also exhibit in a contemporary work [4] inthe context of 3D Navier-Stokes equations. Finally, we make a discussion on thelocal and global existence problem in the 2D case.

Weak-strong uniqueness in weighted $L^2$ spaces and weak suitable solutions in local Morrey spaces for the MHD equations