Relativistic hydrodynamics of magnetic and dielectric fluids in interaction with the electromagnetic field

The semirelativistic hydrodynamic equations of motion of de Groot and Mazur [Non-Equilibrium Thermodynamics (North-Holland, Amsterdam, 1962)] for a fluid with polarization and magnetization are derived from the relativistic energy-momentum conservation equation, mass conservation, and Maxwell's equations on the basis of a systematic expansion in inverse powers of the velocity of light. A modification of the de Groot-Suttorp field energy-momentum tensor [de Groot and Suttorp, Foundations of Electrodynamics (North-Holland, Amsterdam, 1972)] based on a shift of terms to the internal energy density of the fluid yields relatively simple expressions for energy density, energy current density, momentum density, and stress tensor.