Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Reduced models for electron magnetohydrodynamics: Well-posedness and singularity formation
HTML articles powered by AMS MathViewer

by Mimi Dai;
Trans. Amer. Math. Soc. 378 (2025), 3981-4009
DOI: https://doi.org/10.1090/tran/9427
Published electronically: March 25, 2025

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
Similar Articles
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