تقرير
Asymmetry of MHD equilibria for generic adapted metrics
| العنوان: | Asymmetry of MHD equilibria for generic adapted metrics |
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| المؤلفون: | Cardona, Robert, Duignan, Nathan, Perrella, David |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics Mathematical Physics Physics (Other) |
| مصطلحات موضوعية: | Mathematics - Differential Geometry, Mathematical Physics, Physics - Plasma Physics, 35Q31, 76W05 (Primary) 53C20, 53B20, 53C80 (Secondary) |
| الوصف: | 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 in $M$ 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. Comment: 36 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2312.14368 |
| رقم الأكسشن: | edsarx.2312.14368 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |