Axisymmetric diffeomorphisms and ideal fluids on Riemannian 3-manifolds

Leandro Lichtenfelz, Gerard Misiolek, Stephen C. Preston

We study the Riemannian geometry of 3D axisymmetric ideal fluids. We prove that the $L^2$ exponential map on the group of volume-preserving diffeomorphisms of a $3$-manifold is Fre…