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Local Well-posedness of the Incompressible Current-Vortex Sheet Problems

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arxiv 2309.03534 v2 pith:63XLE5H3 submitted 2023-09-07 math.AP

Sicheng Liu , Zhouping Xin This is my paper · ORCID
classification math.AP
keywords current-vortexconditionincompressiblelocalmotionproblemssheetsheets
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We prove the local well-posedness of the incompressible current-vortex sheet problems in standard Sobolev spaces under the surface tension or the Syrovatskij condition, which shows that both capillary forces and large tangential magnetic fields can stabilize the motion of current-vortex sheets. Furthermore, under the Syrovatskij condition, the vanishing surface tension limit is established for the motion of current-vortex sheets. These results hold without assuming the interface separating the two plasmas being a graph.

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  1. Sharp well-posedness for the free boundary MHD equations

    math.AP 2024-12 conditional novelty 8.0 of 10

    Free boundary incompressible magnetohydrodynamics is shown to be well-posed at the sharp low-regularity scale s > d/2 + 1, with first uniqueness and smooth-solution construction results in a new state space.

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