Well-posedness for the 1D cubic nonlinear Schrödinger equation in Lp, p>2. (January 2023)

• Record Type: Journal Article
• Authors: Hyakuna, Ryosuke
• Is Part Of: Nonlinear analysis. Volume 226(2023)
• Publication Date: 2023-01
• Subjects: 35Q55; Nonlinear Schrödinger equation -- Well-posedness -- Lp-data; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2022.113154
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, local well-posedness is shown for the one dimensional cubic nonlinear Schrödinger equation in L p -spaces for 2 < p < 4, which generalizes a classical result for p = 2 by Y. Tsutsumi in the direction opposite to the previous work for 1 < p < 2 by Y. Zhou. As a consequence, a local theory of solutions is developed for a class of data which decay more slowly than square integrable functions. Regularity properties of the local solutions in the L p -based Sobolev spaces and Stricharz spaces are also proved.