In this paper we study equations of magnetic hydrodynamics with a stress tensor. We interpret this system as the generalized Euler equation associated with an Abelian extension of the Lie algebra of vector fields with a nontrivial 2-cocycle. We use the Lie algebra approach to prove the energy conservation law and the conservation of cross-helicity.

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Journal Journal of Mathematical Physics
Billig, Y. (2005). Magnetic hydrodynamics with asymmetric stress tensor. Journal of Mathematical Physics, 46(4). doi:10.1063/1.1857065