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 Alonso Orán et al. (The three dimensional magneto-hydrostatic equations with Grad–Rubin boundary value, 2023) and Alonso-Orán and Velázquez (Math Ann 388:2387–2472, 2024), 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 than in Alonso Orán et al. (2023) and Alonso-Orán and Velázquez (2024). 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.