Reduced models for electron magnetohydrodynamics: Well-posedness and singularity formation
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- by Mimi Dai;
- Trans. Amer. Math. Soc. 378 (2025), 3981-4009
- DOI: https://doi.org/10.1090/tran/9427
- Published electronically: March 25, 2025
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Abstract:
We propose one-dimensional reduced models for the three-dimensional electron magnetohydrodynamics which involves a highly nonlinear Hall term with intricate structure. The models contain nonlocal nonlinear terms which are more singular than that of the one-dimensional models for the Euler equation and the surface quasi-geostrophic equation. Local well-posedness is obtained in certain circumstances. Moreover, for a model with nonlocal transport term, we show that singularity develops in finite time for a class of initial data.References
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Bibliographic Information
- Mimi Dai
- Affiliation: Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, Illinois 60607
- MR Author ID: 941612
- ORCID: 0000-0002-3193-2228
- Email: mdai@uic.edu
- Received by editor(s): March 27, 2023
- Received by editor(s) in revised form: May 14, 2024
- Published electronically: March 25, 2025
- Additional Notes: The author was partially supported by the NSF grants DMS–1815069 and DMS–2009422, and the von Neumann Fellowship at the Institute for Advanced Study.
- © Copyright 2025 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 378 (2025), 3981-4009
- MSC (2020): Primary 35Q35, 76B03, 76D03, 76W05
- DOI: https://doi.org/10.1090/tran/9427