On the ill-posedness of the 5th-order Gardner equation
Analysis of PDEs
2019-09-10 v2
Abstract
We present ill-posedness results for the initial value problem (IVP) of the 5th-order Gardner equation. We use new breather solutions discovered for this higher order Gardner equation to measure the regularity of the Cauchy problem in Sobolev spaces . We find the sharp Sobolev index under which the local well-posedness of the problem is lost, meaning that the dependence of 5th order Gardner solutions upon initial data fails to be continuous.
Keywords
Cite
@article{arxiv.1810.10434,
title = {On the ill-posedness of the 5th-order Gardner equation},
author = {Miguel A. Alejo and Eleomar Cardoso},
journal= {arXiv preprint arXiv:1810.10434},
year = {2019}
}
Comments
Some typos corrected and references updated