On the existence of force-free magnetic fields with small nonconstant \(\alpha\) in exterior domains
type: Item
instance of: scholarly article
title: On the existence of force-free magnetic fields with small nonconstant \(\alpha\) in exterior domains
zbMATH Open document ID: 0964.76096
published in: Communications in Mathematical Physics
publication date: 2000-10-08T00:00:00Z
review text: This paper is mainly motivated by astrophysical phenomena, e.g. coronal loops or magnetic arcades of the Sun or solar flares which are modelled by magnetic flux tubes from the solar convection zone into the coronal space. Typically, in stellar atmospheres the magnetic fields have to be force-free. Force-free magnetic fields are characterized by the alignment of magnetic field to the electric current, \(Bj = \alpha B\), leading to vanishing Lorentz force. Here the authors show that for small (in the Hölder norm) \(\alpha\) which is constant along the magnetic flux lines but varies across the magnetic tube, there exist magnetic fields for which the magnetic tubes start and end on a simply connected compact surface. The proof generalizes and avoids some shortcomings of a previous analysis of \textit{M. Bineau} [Commun. Pure Appl. Math. 25, 77-84 (1972; Zbl 0226.35016)], and uses an iteration scheme. At each step the authors need the solutions of an intial value problem for linear first-order differential equations, and a Neumann boundary value problem for inhomogeneous harmonic vector fields.
Mathematics Subject Classification ID: 76W05
Mathematics Subject Classification ID: 35Q60
Mathematics Subject Classification ID: 85A30
zbMATH DE Number: 1514629
zbMATH Keywords: coronal loops
zbMATH Keywords: magnetic arcades
zbMATH Keywords: solar flares
zbMATH Keywords: magnetic flux tubes
zbMATH Keywords: solar convection zone
zbMATH Keywords: initial value problem
zbMATH Keywords: linear first-order differential equations
zbMATH Keywords: Neumann boundary value problem
zbMATH Keywords: inhomogeneous harmonic vector fields
author: Ralf Kaiser
author: Michael Neudert
author: Wolf von Wahl
MaRDI profile type: Publication
full work available at URL: s002200050804
OpenAlex ID: W2021474810
DOI: 10.1007/S002200050804
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description: scientific article; zbMATH DE number 1514629