Asymmetry of MHD Equilibria for Generic Adapted Metrics

IF 2.6 1区 数学 Q1 MATHEMATICS, APPLIED
Robert Cardona, Nathan Duignan, David Perrella
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引用次数: 0

Abstract

Ideal magnetohydrodynamic (MHD) equilibria on a Riemannian 3-manifold satisfy the stationary Euler equations for ideal fluids. A stationary solution X admits a large set of “adapted” metrics on M for which X solves the corresponding MHD equilibrium equations with the same pressure function. We prove different versions of the following statement: an MHD equilibrium with non-constant pressure on a compact three-manifold with or without boundary admits no continuous Killing symmetries for an open and dense set of adapted metrics. This contrasts with the classical conjecture of Grad which loosely states that an MHD equilibrium on a toroidal Euclidean domain in \({\mathbb {R}}^3\) with pressure function foliating the domain with nested toroidal surfaces must admit Euclidean symmetries.

一般自适应度量的MHD均衡的不对称性
黎曼3流形上的理想磁流体动力学平衡满足理想流体的稳态欧拉方程。一个平稳解X允许M上有大量的“适应”度量,X用相同的压力函数求解相应的MHD平衡方程。我们证明了以下陈述的不同版本:紧致三流形上有边界或无边界的非定压MHD平衡对于一组开放和密集的自适应度量不允许连续的Killing对称。这与Grad的经典猜想形成了对比,后者松散地陈述了在\({\mathbb {R}}^3\)的环面欧几里得区域上的MHD平衡,该区域具有嵌套环面表面的压力函数片理,必须承认欧几里得对称性。
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来源期刊
CiteScore
5.10
自引率
8.00%
发文量
98
审稿时长
4-8 weeks
期刊介绍: The Archive for Rational Mechanics and Analysis nourishes the discipline of mechanics as a deductive, mathematical science in the classical tradition and promotes analysis, particularly in the context of application. Its purpose is to give rapid and full publication to research of exceptional moment, depth and permanence.
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