On energy conservation in extended magnetohydrodynamics
  A systematic study of energy conservation for extended magnetohydrodynamic (MHD) models that include Hall terms and electron inertia is performed. It is observed that commonly used models do not conserve energy in the ideal limit, i.e., when viscosity and resistivity are neglected. In particular, a term in the momentum equation that is often neglected is seen to be needed for conservation of energy. 
Keiji Kimura and P. J. Morrison
physics.plasm-ph astro-ph.SR physics.space-ph