The three dimensional magneto-hydrostatic equations with Grad-Rubin boundary value
Analysis of PDEs
2024-02-06 v1 Mathematical Physics
math.MP
Abstract
In this work, we study the well-posedness of the three dimensional magneto-hydrostatic equation under Grad-Rubin boundary value conditions. The proof relies on a fixed point argument to construct solutions to an elliptic-hyperbolic problem in a perturbative regime by means of pseudo-differential operators with symbols with limited regularity in H\"older spaces. As a byproduct, the employed technique in this work is more flexible and simplifies the arguments of the proof for the previous two-dimensional setting.
Cite
@article{arxiv.2402.03078,
title = {The three dimensional magneto-hydrostatic equations with Grad-Rubin boundary value},
author = {Diego Alonso-Orán and Daniel Sánchez-Simón del Pino and Juan J. L. Velázquez},
journal= {arXiv preprint arXiv:2402.03078},
year = {2024}
}