Existence of vortex rings in Beltrami flows

2020/08/21 by Ken Abe, Abe, Ken · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Waves and Solitons

paper · doi:10.48550/arxiv.2008.09345

openalex publication_date 2020/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct traveling wave solutions to the 3d Euler equations by axisymmetric Beltrami fields with a non-constant proportionality factor. They form a vortex ring with nested invariant tori consisting of level sets of the proportionality factor.

Citations

• Wave breaking for nonlinear nonlocal shallow water equations
• Stability of Lamb dipoles

Cited by

• Solutions to the two-dimensional steady incompressible Euler equations in an annulus

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