We prove global well-posedness of solution to the 3D incompressible Hall-magnetohydrodynamics (Hall-MHD) equations, where the initial data is in critical Besov space. Since the initial vertical velocity may be large enough, our work improves some recent results in WanZ2,WZ19.
"Global well-posedness of the 3D incompressible Hall-MHD equations for small initial data in certain Besov spaces." Rocky Mountain J. Math. 50 (6) 2127 - 2139, December 2020. https://doi.org/10.1216/rmj.2020.50.2127