This paper concerns regularity criteria for the $2$D generalized MHD system and shows that, if we can control the Besov norm of the vorticity and/or the current density, then the solution is, in fact, smooth. This improves the recent result of Jiang, Wang, and Zhou (2016).
"Remarks on regularity criteria for the 2D generalized MHD system in Besov spaces." Rocky Mountain J. Math. 48 (8) 2785 - 2795, 2018. https://doi.org/10.1216/RMJ-2018-48-8-2785