In this paper we deal with the existence, regularity and Beltrami field property of magnetic energy minimisers under a helicity constraint. We in particular tackle the problem of characterising local as well as global minimisers of the given minimisation problem. Further we generalise Arnold’s results concerning the problem of finding the minimum magnetic energy in an orbit of the group of volume-preserving diffeomorphisms to the setting of abstract manifolds with boundary.

中文翻译：

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在任意螺旋度类中具有边界的定向紧凑黎曼 3 流形上磁能最小化器的存在和表征

在本文中，我们讨论了在螺旋度约束下磁能最小化器的存在性、规律性和贝尔特拉米场性质。我们特别解决了表征给定最小化问题的局部和全局最小化器的问题。进一步，我们将阿诺德关于在体积保持微分同胚群的轨道中找到最小磁能问题的结果推广到具有边界的抽象流形的设置。