On the well-posedness of the inviscid 2D Boussinesq equation

Abstract

In this paper we consider the inviscid 2D Boussinesq 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, $(u(0),\theta (0))\mapsto (u(T),\theta (T))$, is nowhere locally uniformly continuous.