On the Grad–Rubin boundary value problem for the two-dimensional magneto-hydrostatic equations
In 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 t...
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| Veröffentlicht in: | Mathematische annalen 2024-01, Vol.388 (3), p.2387-2472 |
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| container_title | Mathematische annalen |
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| creator | Alonso-Orán, Diego Velázquez, Juan J. L. |
| description | In 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. |
| doi_str_mv | 10.1007/s00208-023-02582-1 |
| format | Article |
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| subjects | Boundary value problems Euler-Lagrange equation Mathematical analysis Mathematics Mathematics and Statistics Nuclear energy |
| title | On the Grad–Rubin boundary value problem for the two-dimensional magneto-hydrostatic equations |
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