Solvability of MHS equations with Grad-Rubin boundary conditions in general 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-Orán and J. L. L. Velázquez, 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.

60 pages, 1 figure