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Abstract We consider the well-posedness of the surface quasi-geostrophic (SQG) front equation. Hunter–Shu–Zhang (2021Pure Appl. Anal.3403–72) established well-posedness under a small data condition as well as a convergence condition on an expansion of the equation’s nonlinearity. In the present article, we establish unconditional large data local well-posedness of the SQG front equation, while also improving the low regularity threshold for the initial data. In addition, we establish global well-posedness theory in the rough data regime by using the testing by wave packet approach of Ifrim–Tataru.
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This content will become publicly available on November 22, 2025
Global Well-Posedness for Supercritical SQG With Perturbations of Radially Symmetric Data
Abstract We study the global well-posedness of the supercritical dissipative surface quasi-geostrophic (SQG) equation, a key model in geophysical fluid dynamics. While local well-posedness is known, achieving global well-posedness for large initial data remains open. Motivated by enhanced decay in radial solutions, we aim to establish global well-posedness for small perturbations of potentially large radial data. Our main result shows that for small perturbations of radial data, the SQG equation admits a unique global solution.
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- Award ID(s):
- 2350129
- PAR ID:
- 10608609
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- International Mathematics Research Notices
- Volume:
- 2024
- Issue:
- 24
- ISSN:
- 1073-7928
- Page Range / eLocation ID:
- 14655 to 14661
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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