Multi-Symplectic Magnetohydrodynamics: II, Addendum and Erratum
arXiv:1506.08322 · doi:10.1017/S0022377815001415
Abstract
A recent paper arXiv:1312.4890 on multi-symplectic magnetohydrodynamics (MHD) using Clebsch variables in an Eulerian action principle with constraints is further extended. We relate a class of symplecticity conservation laws to a vorticity conservation law, and provide a corrected form of the Poincaré-Cartan differential form formulation of the system. We also correct some typographical errors (omissions) in arXiv:1312.4890. We show that the vorticity-symplecticity conservation law, that arises as a compatibility condition on the system, expressed in terms of the Clebsch variables is equivalent to taking the curl of the conservation form of the MHD momentum equation. We use the Cartan-Poincaré form to obtain a class of differential forms that represent the system using Cartan's geometric theory of partial differential equations.
12 pages
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