Existence And Stability Of Global Large Strong Solutions For The Hall-mhd System

Abstract

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.