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The helicity uniqueness conjecture in 3D hydrodynamics

By Boris Khesin and others
We prove that the helicity is the only regular Casimir function for the coadjoint action of the volume-preserving diffeomorphism group SDiff(M)\text{SDiff}(M) on smooth exact divergence-free vector fields on a closed three-dimensional manifold MM. More precisely, any regular C1C^1 functional defined on the space of CC^\infty (more generally, CkC^k, k4k\ge 4)... Show more
March 12, 2020
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The helicity uniqueness conjecture in 3D hydrodynamics
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