  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}.

Analysis of PDEs