Low regularity well-posedness for the generalized surface quasi-geostrophic front equation
Analysis of PDEs
2026-04-15 v1
Abstract
We consider the well-posedness of the generalized surface quasi-geostrophic (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 non-periodic 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-Tataru.
Keywords
Cite
@article{arxiv.2311.07551,
title = {Low regularity well-posedness for the generalized surface quasi-geostrophic front equation},
author = {Albert Ai and Ovidiu-Neculai Avadanei},
journal= {arXiv preprint arXiv:2311.07551},
year = {2026}
}
Comments
47 pages. This paper is companion to arXiv:2310.20143 and arXiv:2212.00117, and contains structural overlap