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

TL;DR

This paper constructs a steady Euler flow on the 3-sphere with special integrals, linking it to a critical point of the Faddeev-Skyrme model, revealing new geometric and physical insights.

Contribution

It introduces a novel steady Euler flow on the 3-sphere with two independent first integrals, connecting fluid dynamics with the Faddeev-Skyrme model.

Findings

Flow has two independent first integrals.

Flow is tangent to fibers of an almost submersion.

Submersion is a critical point for the Faddeev-Skyrme model.

Abstract

We present a steady Euler flow on the round 3-sphere whose velocity vector field has the property of having two independent first integrals, being tangent to the fibres 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.