Solvability of MHS equations with Grad-Rubin boundary conditions in general domains

TL;DR

This paper extends the solvability theory of magnetohydrostatic equations with Grad-Rubin boundary conditions to more general and physically relevant domains, beyond simple geometries previously studied.

Contribution

It develops a new theoretical framework that enables solving these boundary value problems in a broader class of domains, including those near circles or spheres.

Findings

Successfully extended solvability to complex domains

Applied theory to physically relevant geometries

Provided conditions for solvability in near-spherical domains

Abstract

In this paper we study the solvability of the magnetohydrostatic equations with Grad-Rubin boundary conditions in general domains. Earlier results for this problem were obtained in the recent years by D. Alonso-Or\'an and J. L. L. Vel\'azquez, where particularly simple geometries were considered. In this article we develop a theory that allows to solve these boundary value problems for a larger class of domains. We will give precise applications to more physically relevant situations, like the case of the space between two circumferences or spheres and domains close to them.