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.
Chen et al. (Wed,) studied this question.