Ill-posedness results for generalized Boussinesq equations
Analysis of PDEs
2012-10-16 v2
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.
Keywords
Cite
@article{arxiv.1209.0998,
title = {Ill-posedness results for generalized Boussinesq equations},
author = {Dan-Andrei Geba and A. Alexandrou Himonas and David Karapetyan},
journal= {arXiv preprint arXiv:1209.0998},
year = {2012}
}
Comments
12 pages. Based on the comments received from Nobu Kishimoto, we amended the original results which claimed the discontinuity of the solution map to new ones proving the loss of smoothness for the flow map