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On the existence of non-linear force-free fields in three-dimensional domains

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Abstract.

Non-linear force-free fields (or Beltrami fields) are three-component divergence-free fields solutions of the equation curl B x B = 0. The aim of this paper is to prove existence of solutions of a corresponding boundary value problem in a simply or multiply connected domain of \({\Bbb R}^3\). The proof is based on a fixed point procedure coupled with a singular perturbation skill.

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Authors and Affiliations

  1. Université de Pau et des pays de l'Adour, Département de mathématiques, I.P.R.A., Avenue de l'Université, 64000, Pau, France, e-mail: Tahar.Boulmezaoud@univ-pau.fr, , , , , , FR

    T. Z. Boulmezaoud

  2. Centre de Physique Théorique, Ecole Polytechnique, 91128 Palaiseau Cedex, France, e-mail: amari@cpht.polytechnique.fr, , , , , , FR

    T. Amari

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  1. T. Z. Boulmezaoud
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  2. T. Amari
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Received: 16 March 1999; revised: January 4, 2000

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Boulmezaoud, T., Amari, T. On the existence of non-linear force-free fields in three-dimensional domains. Z. angew. Math. Phys. 51, 942–967 (2000). https://doi.org/10.1007/PL00001531

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  • DOI: https://doi.org/10.1007/PL00001531

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