Global Weak Solutions to the Density-Dependent Hall-Magnetohydrodynamics System

We are concerned with the global existence of finite energy weak solutions to 3D density-dependent magnetohydrodynamics system with Hall-effect set in a general smooth bounded domain. The perfectly conducting wall boundary condition is imposed on the magnetic field. Due to the degeneracy of Hall-effect term (a higher-order trilinear term) in vacuum, we assumed initial density lies in the bounded function space and having a positive lower bound....