Magnetic hydrodynamics with asymmetric stress tensor

TL;DR

This paper explores magnetic hydrodynamics equations with an asymmetric stress tensor, using Lie algebra methods to establish energy and cross-helicity conservation laws.

Contribution

It introduces a generalized Euler equation framework for magnetic hydrodynamics with asymmetric stress tensors via Lie algebra extensions.

Findings

Proves energy conservation law for the system

Establishes conservation of cross-helicity

Provides a Lie algebra interpretation of the equations

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.