Global Well‐Posedness of 3D Incompressible Inhomogeneous Hall‐Magnetohydrodynamics System With Density‐Dependent Viscosity

ABSTRACT This paper examines the global‐in‐time existence and uniqueness of solutions for the inhomogeneous incompressible Hall‐MHD system with bounded density. In the three‐dimensional case, assuming that the initial density is a small perturbation of a positive constant in the norm, the initial velocity data with , we prove global well‐posedness for small initial velocity and magnetic fields in critical Besov spaces. Our result extends the corresponding one in [29].