A note on global existence of weak solutions to the compressible magnetohydrodynamic equations with Coulomb force

In this note, for the case of (9+33)/12<γ⩽4/3, we prove the existence of global-in-time finite energy weak solution of the equations of a two-dimensional magnetohydrodynamics with Coulomb force, where γ denotes the adiabatic exponent. The value (9+33)/12 is the optimal lower bound of γ to establish global-in-time finite energy weak solution under current frame.