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.