Ill-posedness results for generalized Boussinesq equations

Abstract

In this article we present ill-posedness results for generalized Boussinesq equations, which incorporate also the ones obtained by the authors for the classical "good" Boussinesq equation (arXiv:1202.6671). More precisely, we show that the associated flow map is not smooth for a range of Sobolev indices, thus providing a threshold for the regularity needed to perform a Picard iteration for these problems.