On the Grad-Rubin boundary value problem for the two-dimensional magneto-hydrostatic equations
Analysis of PDEs
2022-03-09 v1 Mathematical Physics
math.MP
Abstract
In this work, we study the solvability of a boundary value problem for the magneto-hydrostatic equations originally proposed by Grad and Rubin in the late 50's. The proof relies on a fixed point argument which combines the so-called current transport method together with H\"older estimates for a class of non-convolution singular integral operators. The same method allows to solve an analogous boundary value problem for the steady incompressible Euler equations.
Cite
@article{arxiv.2203.04062,
title = {On the Grad-Rubin boundary value problem for the two-dimensional magneto-hydrostatic equations},
author = {Diego Alonso-Orán and Juan J. L. Velázquez},
journal= {arXiv preprint arXiv:2203.04062},
year = {2022}
}
Comments
62 pages