Uniqueness for SQG patch solutions

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.

arXiv comment29 pages, main result added in the introduction in terms of weak solutions, proofs and comments expanded, one section with uniqueness for contour equation (7)