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 $\text{SDiff}(M)$ on smooth exact divergence-free vector fields on a closed three-dimensional manifold $M$. More precisely, any regular $C^1$ functional defined on the space of $C^\infty$ (more generally, $C^k$, $k\ge 4$)... Show more

March 12, 2020

Loading full text...

Similar articles

Loading recommendations...

x1

The helicity uniqueness conjecture in 3D hydrodynamics

Click on play to start listening