A remark on the Half wave Schr\"odinger equation in the energy space

Isao Kato

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arXiv · 2203.00425

A remark on the Half wave Schr\"odinger equation in the energy space

Isao Kato

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Abstract

We investigate the Cauchy problem for the half wave Schr\"odinger equation in the energy space. We derive the local well-posedness in the energy space for the odd power type nonlinearities under certain additional assumption for the initial data, namely $\hat{u}_0 \in L^1_{\xi, \eta}(\mathbb{R}^2)$.

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Isao Kato. 2022-03-01. A remark on the Half wave Schr\"odinger equation in the energy space. https://arxiv.org/abs/2203.00425

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