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Global nonlinear stability of the plasma-vacuum free boundary problem for the 2D ideal incompressible MHD

  • Yuan Cai
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Abstract

We address the plasma-vacuum interface problem in the two dimensional space. The plasma region is governed by the ideal incompressible magnetohydrodynamic equations. The vacuum region is described by the pre-Maxwell dynamics, with the unknowns set to zero for simplicity. This is a free boundary problem of ideal Euler type equations. Under the strong horizontal magnetic field in the plasma region, we prove the global in time nonlinear stability of the two dimensional plasma-vacuum interface. The proof relies on understanding the interplay between the dynamics of the fluids inside the domain and those on the free interface, as well as the inherent structures of the problem.

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Cite

BibTeXRIS
BibTeX
@misc{cai2026global,
  title = {{Global nonlinear stability of the plasma-vacuum free boundary problem for the 2D ideal incompressible MHD}},
  author = {Yuan Cai},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.10009},
  eprint = {2609.10009},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.10009},
}
RIS
TY  - UNPB
TI  - Global nonlinear stability of the plasma-vacuum free boundary problem for the 2D ideal incompressible MHD
AU  - Yuan Cai
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2609.10009
UR  - https://arxiv.org/abs/2609.10009
AB  - We address the plasma-vacuum interface problem in the two dimensional space. The plasma region is governed by the ideal incompressible magnetohydrodynamic equations. The vacuum region is described by the pre-Maxwell dynamics, with the unknowns set to zero for simplicity. This is a free boundary problem of ideal Euler type equations. Under the strong horizontal magnetic field in the plasma region, we prove the global in time nonlinear stability of the two dimensional plasma-vacuum interface. The proof relies on understanding the interplay between the dynamics of the fluids inside the domain and those on the free interface, as well as the inherent structures of the problem.
ER  -