Low regularity solutions for the surface quasi-geostrophic front equation

TL;DR

This paper investigates the low regularity well-posedness of the surface quasi-geostrophic front equation, revealing a null structure that enables improved local and global solutions.

Contribution

It identifies a null structure in the SQG front equation and applies normal form analysis to enhance well-posedness results at low regularity levels.

Findings

Established improved local well-posedness

Proved global well-posedness under certain conditions

Identified null structure in SQG 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.