Conservation laws of magnetohydrodynamics and their symmetry transformation properties

Abstract

All kinematic conservation laws along with their symmetry transformation properties are derived for the system of magnetohydrodynamic equations governing incompressible viscous plasmas (or any other conducting fluid) in which the dynamic and magnetic viscosities are constant. Reductions of this system under translation symmetries, axial rotation symmetries, and helical symmetries are considered. For each reduced system, all kinematic conservation laws and point symmetries are obtained. The results yields several new conservation laws which are expected to be relevant for physical applications of magnetohydrodynamics.