An ill-posedness result for the Boussinesq equation

Abstract

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 $s<-1/2$.

Based on the comments received from Nobu Kishimoto, the original version has been amended and incorporated with the results of arXiv:1209.0998

References in corpus (2)

• Local solutions in Sobolev spaces with negative indices for the "good" Boussinesq equation
• Sharp well-posedness and ill-posedness results for a quadratic non-linear Schrödinger equation

Cited by in corpus (1)

• Ill-posedness results for generalized Boussinesq equations