Global wellposedness for Hall-MHD equations

On well-posedness of generalized Hall-magneto-hydrodynamics

“…In [6], Chae and Lee established a blow-up criterion and a small data global existence result. In addition, local well-posedness results can be found in the works by Dai [12,13], and global existence results for small data were also proved by Wan and Zhou [40] as well as by Kwak and Lkhagvasuren [29]. For various regularity criteria, readers are referred to [11,16,17,25,42,46,47,48,50].…”

On 3D Hall-MHD Equations with Fractional Laplacians: Global Well-Posedness

“…Of interests to present paper, Chae et al [7] established global well-posedness of classical solutions for (1.3) with small initial data; Chae and Lee [8] improved the result of [7] under weaker smallness assumptions on initial data; Fan et al [17] studied global well-posedness of axisymmetric solutions with large initial data; and Li et al [27] and Zhang [42] constructed a class of (non-axisymmetric) large initial data and proved global wellposedness of classical solutions. There are also works dealing with low regularity solutions, extensibility criteria, and large-time asymptotic behavior for (1.3), and we refer the readers to [1,10,11,16,21,25,34,40] for more information in these directions.…”

Global Existence of Smooth Solutions to Three Dimensional Hall-MHD System with Mixed Partial Viscosity

“…As a byproduct, a class of global strong solutions was also obtained with large velocities and small initial magnetic fields. Global well-posedness of mild solutions in Lei-Lin function spaces (see [19]) was established in [20]. Global well-posedness and analyticity of mild solutions was obtained by Duan [21].…”