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.