Comment by troystribling

Magnetohydrodynamics (MHD) is the combination of Maxwell's Equations in a moving frame of reference and The Navier Stokes Equation. So it includes both the impact of inertial and electromagnetic forces of the flow. MHD is the long wavelength limit of kinetic (particle) plasma theory. The Earths core has in the past been modeled as an MHD fluid but it is usually assumed to be incompressible. I am not aware of compressible models but I have not worked in this field in a decade.