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Abstract We prove the existence and uniqueness of global smooth solutions of the critical dissipative SQG equation in bounded domains in . We introduce a new methodology of transforming the single nonlocal nonlinear evolution equation in a bounded domain into an interacting system of extended nonlocal nonlinear evolution equations in the whole space. The proof then uses the method of the nonlinear maximum principle for nonlocal operators in the extended system.
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This content will become publicly available on June 1, 2026
Reduced models for electron magnetohydrodynamics: Well-posedness and singularity formation
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.
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- Award ID(s):
- 2308208
- PAR ID:
- 10596693
- Publisher / Repository:
- American Mathematical Society
- Date Published:
- Journal Name:
- Transactions of the American Mathematical Society
- Volume:
- 378
- Issue:
- 1093
- ISSN:
- 0002-9947
- Page Range / eLocation ID:
- 3981 to 4009
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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