Low regularity well-posedness for the generalized surface quasigeostrophic front equation
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.
Fields of Study & Subjects
Advanced Mathematical Physics Problems
Navier-Stokes equation solutions
Publication details
- Journal / source
- Pure and Applied Analysis
- Publisher
- Mathematical Sciences Publishers
- Volume
- 8
- Issue
- 2
- Pages
- 271–329
- Publication date
- 9 April 2026
- Language
- EN