Magnetic hydrodynamics with asymmetric stress tensor

Abstract

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 non-trivial 2-cocycle. We use the Lie algebra approach to prove the energy conservation law and the conservation of cross-helicity.

References in corpus (4)

• Principal Vertex Operator Representations for Toroidal Lie Algebras
• Lowest-energy representations of non-centrally extended diffeomorphism algebras
• Energy-momentum tensor for the toroidal Lie algebras
• Abelian Extensions of the Group of Diffeomorphisms of a Torus

Cited by in corpus (5)

• Geodesic Equations on Diffeomorphism Groups
• A class of three-dimensional gyroviscous magnetohydrodynamic models
• Non-Riemannian geometrical asymmetrical damping stresses on the Lagrange instability of shear flows
• Representations of toroidal extended affine Lie algebras
• A Wakimoto type realization of toroidal ${\mathfrak{sl}}_{n+1}$