Steady Euler flows on the 3-sphere and other Sasakian 3-manifolds

Abstract

We present new steady Euler solutions on the (round) 3-sphere, that bifurcate from an ansatz proposed by Khesin, Kuksin and Peralta-Salas, showing that these previously known solutions are not isolated. We also extend this ansatz to any Sasakian 3-manifold, such as the Heisenberg group and $SL(2,\mathbb{R})$.

12 pages. Improved presentation. Matches published version

References in corpus (3)

• Global, local and dense non-mixing of the 3D Euler equation
• Tight Beltrami fields with symmetry
• Energy minimizing Beltrami fields on Sasakian 3-manifolds