Existence of ideal magnetofluid equilibria without continuous Euclidean symmetries

Abstract

We study the existence of steady solutions of ideal magnetofluid systems (ideal MHD and ideal Euler equations) without continuous Euclidean symmetries. It is shown that all nontrivial magnetofluidostatic solutions are locally symmetric, although the symmetry is not necessarily an Euclidean isometry. Furthermore, magnetofluidostatic equations admit both force-free (Beltrami type) and non-force-free (with finite pressure gradients) solutions that do not exhibit invariance under translations, rotations, or their combination. Examples of smooth solutions without continuous Euclidean symmetries in bounded domains are given. Finally, the existence of square integrable solutions of the tangential boundary value problem without continuous Euclidean symmetries is proved.

References in corpus (4)

• Computation of multi-region relaxed magnetohydrodynamic equilibria
• Beltrami fields with a nonconstant proportionality factor are rare
• Local Representation and Construction of Beltrami Fields
• Local representation and construction of Beltrami fields II. Solenoidal Beltrami fields and ideal MHD equilibria

Cited by in corpus (2)

• Quasisymmetric magnetic fields in asymmetric toroidal domains
• Symmetric Ideal Magnetofluidostatic Equilibria with Non-Vanishing Pressure Gradients in Asymmetric Confinement Vessels