An ill-posedness result for the Boussinesq equation

Dan-Andrei Geba, A. Alexandrou Himonas, David Karapetyan

Published 2012-02-29, updated 2012-10-15Version 2

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 $s<-1/2$.