A steady Euler flow on the 3-sphere and its associated Faddeev-Skyrme solution

Abstract

We present a steady Euler flow on the round 3-sphere S 3 whose velocity vector field has the remarkable property of having two first integrals, being tangent to the fibers of an almost submersion onto the 2-sphere. This submersion turns out to be a critical point for the quartic Faddeev-Skyrme model with a standard potential.