Existence and stability of global large strong solutions for the   Hall-MHD system
  We consider the 3D incompressible Hall-MHD system and prove a stability theorem for global large solutions under a suitable integrable hypothesis in which one of the parcels is linked to the Hall term. As a byproduct, a class of global strong solutions is obtained with large velocities and small initial magnetic fields. Moreover, we prove the local-in-time well-posedness of $H^{2}$-strong solutions which improves previous regularity conditions on initial data. 
Maicon J. Benvenutti and Lucas C.F. Ferreira
math.AP