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Low regularity well-posedness for the generalized surface quasigeostrophic front equation

Albert Ai and Ovidiu-Neculai Avadanei
Vol. 8 (2026), No. 2, 271–329
DOI: 10.2140/paa.2026.8.271
Abstract

We consider the well-posedness of the generalized surface quasigeostrophic (gSQG) front equation. By using the null structure of the equation via a paradifferential normal form analysis, we obtain balanced energy estimates, which allow us to prove the local well-posedness of the nonperiodic gSQG front equation at a low level of regularity (in the SQG case, at only one-half derivatives above scaling). In addition, we establish global well-posedness for small and localized rough initial data, as well as modified scattering, by using the testing by wave packet approach of Ifrim and Tataru.

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Keywords
gSQG front equation, low regularity, normal forms, paralinearization, modified energies, frequency envelopes, wave packet testing
Mathematical Subject Classification
Primary: 35B65, 35Q35
Milestones
Received: 14 February 2024
Revised: 10 November 2025
Accepted: 4 March 2026
Published: 9 April 2026
Authors
Albert Ai
Beijing International Center for Mathematical Research
Peking University
Beijing
China
Ovidiu-Neculai Avadanei
Department of Mathematics
Yale University
New Haven, CT
United States
© 2026 MSP (Mathematical Sciences Publishers).