Magnetohydrodynamics (MHD) is fluid dynamics that includes the effects of electrical conductivity of the fluids. (Note that it is not a subset of "Hydrodynamics" as that term is generally used, which is to represent fluid dynamics specifically of liquids rather than gases.)
The field was initiated by Hannes Alfvén who coined the word in the 1940s. It more-or-less consists of the combination of fluid dynamics' Navier-Stokes Equations and electrodynamics' Maxwell's Equations.
Applications in astrophysics include modeling Plasma in the Interplanetary Medium and Interstellar Medium as well as star models, both the interior and the Atmosphere. Such a system involving plasma is sometimes termed a Magneto-Plasma System. Other applications include geophysics (the fluid interior of the Earth), engineering and medicine.
In some astrophysical phenomena, the electrical resistance is minor and its MHD can be effectively simplified by ignoring it. The phrase Resistive MHD indicates that electrical resistance is specifically included.
Navier-Stokes Equations (NS Equations)