An ill-posedness result for the Boussinesq equation
  The aim of this article is to prove new ill-posedness results concerning the nonlinear "good" Boussinesq equation, for both the periodic and non-periodic initial value problems. Specifically, we prove that the associated flow map is not continuous in Sobolev spaces $H^s$, for all $s<-1/2$. 
Dan-Andrei Geba, A. Alexandrou Himonas, and David Karapetyan
math.AP