International Mathematics Research Notices ( IF 1.452 ) Pub Date : 2020-02-09 , DOI: 10.1093/imrn/rnz393
Khesin B, Peralta-Salas D, Yang C.

We prove that any regular Casimir in 3D magnetohydrodynamics (MHD) is a function of the magnetic helicity and cross-helicity. In other words, these two helicities are the only independent regular integral invariants of the coadjoint action of the MHD group \$\textrm{SDiff}(M)\ltimes \mathfrak X^*(M)\$, which is the semidirect product of the group of volume-preserving diffeomorphisms and the dual space of its Lie algebra.

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