On the regularity criteria for the 3D axisymmetric Hall-MHD system in Lorentz spaces

The current paper establishes the regularity criteria for the 3D Hall-MHD system in the axisymmetric setting. When the horizontal angular component of the velocity belongs to some Lorentz spaces, then strong solutions to this system can be smoothly extended beyond the possible blow-up time T. It should be pointed out that our result does not need any additional assumption on the magnetic field.