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

Author:

Alonso-Orán DiegoORCID,Velázquez Juan J. L.

Abstract

AbstractIn this work, we study the solvability of a boundary value problem for the magneto-hydrostatic equations originally proposed by Grad and Rubin (Proceedings of the 2nd UN conference on the peaceful uses of atomic energy. IAEA, Geneva, 1958). The proof relies on a fixed point argument which combines the so-called current transport method together with Hölder 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.

Funder

Ministerio de Ciencia, Innovación y Universidades

Deutsche Forschungsgemeinschaft

Publisher

Springer Science and Business Media LLC

Subject

General Mathematics

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