  We are concerned with the global existence of finite energy weak solutions to
3D density-dependent magnetohydrodynamics (MHD) 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 tri-linear term) in vacuum, we assumed initial density lies
in the bounded function space and having a positive lower bound. Particularly,
these bounds are preserved by the density transport equation which helps yield
a satisfying compactness argument of the magnetic field.
