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March 26, 2026Open Access

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

Key Points

The aim is to explore the solvability of magnetohydrostatic equations with Grad–Rubin boundary conditions in more complex domains.
Developed a new theoretical framework for solving magnetohydrostatic equations.
Applied the theory to various physical geometries, including the space between circles or spheres.
Compared results with previous studies to show advancements in domain applicability.
Established that more complex geometries are solvable compared to earlier studies.
Provided precise applications that enhance understanding of physical scenarios.
Demonstrated the broader applicability of existing mathematical theories in new domains.

Abstract

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.

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Pino et al. (Tue,) studied this question.

synapsesocial.com/papers/69c4cc75fdc3bde448917c1c https://doi.org/https://doi.org/10.1007/s00208-026-03411-x

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