Ill-posedness for the Half wave Schr\"odinger equation
Abstract
We study ill-posedness for the half wave Schr\"odinger equation introduced by Xu 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 CCT1. For the critical space, we use the standing wave solution, which was proved the existence by Bahri, Ibrahim and Kikuchi BIK.
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