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VOL. 81 | 2019 Remark on the scattering operator for the quintic nonlinear Dirac equation in one space dimension
Hironobu Sasaki

Editor(s) Keiichi Kato, Takayoshi Ogawa, Tohru Ozawa

Abstract

This paper is concerned with the scattering operator $S$ for the one dimensional Dirac equation with a quintic nonlinearity. It has been proved that $S$ can be defined on a neighborhood of 0 in the Sobolev space $H^\kappa (\mathbb{R};\mathbb{C}^2)$ for any $\kappa > 3/4$. In the present paper, we prove that for any $M \in \mathbb{N}$ and $s \ge \max\{ \kappa,M \}$, there exists some neighborhood $U$ of 0 in the weighted Sobolev space $H^{s,M}(\mathbb{R};\mathbb{C}^2)$ such that $S(U) \subset H^{s,M}(\mathbb{R};\mathbb{C}^2)$.

Information

Published: 1 January 2019
First available in Project Euclid: 31 October 2019

zbMATH: 07176827

Digital Object Identifier: 10.2969/aspm/08110351

Subjects:
Primary: 35G25, 35P25, 35Q55

Rights: Copyright © 2019 Mathematical Society of Japan

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