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arXiv · 2203.04062

On the Grad-Rubin boundary value problem for the two-dimensional magneto-hydrostatic equations

Diego Alonso-Orán·Juan J. L. Velázquez
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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.

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Diego Alonso-Orán, Juan J. L. Velázquez. 2022-03-08. On the Grad-Rubin boundary value problem for the two-dimensional magneto-hydrostatic equations. https://arxiv.org/abs/2203.04062

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