Low regularity solutions for the surface quasi-geostrophic front equation

Abstract

In this article we consider the low regularity well-posedness of the surface quasi-geostrophic (SQG) front equation. Recent work on other quasilinear models, including the gravity water waves system and nonlinear waves, have demonstrated that in presence of a null structure, a normal form analysis can substantially improve the low regularity theory. In the current article, we observe a null structure in the context of SQG fronts, and establish improved local and global well-posedness results.

33 pages. Fixes some minor typos. Sections 8 and 9 are companion to Sections 6 and 7 from arXiv:2212.00117 and contain some overlap