Ill-posedness for the Half wave Schr\"odinger equation
Analysis of PDEs
2021-12-21 v1
Abstract
We study ill-posedness for the half wave Schr\"odinger equation introduced by Xu \cite{Xu}. Ill-posedness is obtained in the super-critical or at the critical space. The proof is based on the argument established by Christ, Colliander and Tao \cite{CCT1}. For the critical space, we use the standing wave solution, which was proved the existence by Bahri, Ibrahim and Kikuchi \cite{BIK}.
Cite
@article{arxiv.2112.10326,
title = {Ill-posedness for the Half wave Schr\"odinger equation},
author = {Isao Kato},
journal= {arXiv preprint arXiv:2112.10326},
year = {2021}
}