Work

Asymmetry of curl eigenfields solving Woltjer's variational problem

Year: 2025

Type: preprint

Abstract: We construct families of rotationally symmetric toroidal domains in $\mathbb R^3$ for which the eigenfields associated to the first (positive) Ampèrian curl eigenvalue are symmetric, and others for which no first eigenfield is symmetric. This implies, in particular, that minimizers of the celebrated Woltjer's variational principle do not need to inherit the rotational symmetry of the domain. This disproves the folk wisdom that the eigenfields corresponding to the lowest curl eigenvalue must be symmetric if the domain is.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2506.21243

Authors: Peralta-Salas, Daniel, Perrella, David, Pfefferlé, David

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4415182853

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