Uniqueness for SQG patch solutions

TL;DR

This paper proves the uniqueness of solutions for the SQG patch problem, building on previous existence results by introducing new tools and perspectives to establish this key property.

Contribution

It provides the first proof of uniqueness for SQG patch solutions using novel methods and insights beyond prior existence proofs.

Findings

Established uniqueness of SQG patch solutions

Developed new analytical tools for the problem

Enhanced understanding of SQG dynamics

Abstract

This paper is about the evolution of a temperature front governed by the Surface quasi-geostrophic equation. The existence part of that program within the scale of Sobolev spaces was obtained by one of the authors [10]. Here we revisit that proof introducing some new tools and points of view which allow us to conclude the also needed uniqueness result.