On the well-posedness of the inviscid SQG equation

Abstract

In this paper we consider the inviscid SQG equation on the Sobolev spaces $H^s({\mathbb{R}}^2)$, $s>2$. Using a geometric approach we show that for any $T>0$ the corresponding solution map, $\theta (0)\mapsto \theta (T)$, is nowhere locally uniformly continuous.