A basis of Casimirs in 3D magnetohydrodynamics

2019/01/14 by Khesin, Boris, Peralta-Salas, Daniel, Yang, Cheng · 1 citation
#Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1901.04404

Abstract

We prove that any regular Casimir in 3D magnetohydrodynamics 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.

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• Nonuniqueness for high-dimensional ideal MHD equations via differential inclusion

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