A Basis of Casimirs in 3D Magnetohydrodynamics. (9th February 2020) - Khesin, Boris; Peralta-Salas, Daniel; Yang, Cheng
Abstract: 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 $SDiff(M)\ltimes \mathfrak X^*(M)$, which is the semidirect product of the group of volume-preserving diffeomorphisms and the dual space of its Lie algebra.