Wellposedness for semirelativistic Schrödinger equation with power-type nonlinearity. (January 2019)

• Record Type: Journal Article
• Authors: Shi, Qihong; Peng, Congming
• Is Part Of: Nonlinear analysis. Volume 178(2019)
• Page Start: 133
• Page End: 144
• Publication Date: 2019-01
• Subjects: Semirelativistic equation -- Cubic nonlinearity -- Low regularity -- Wellposedness; 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.2018.07.012
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we employ Bourgain type norm to investigate the wellposedness for the Cauchy problem of one dimensional semirelativistic Schrödinger equation with cubic nonlinearity in space H s . We extend the previous existence result to the space regularity s ≥ 1 ∕ 4 . Moreover, we point out the persistence of the solution in different regularity space is uniform by an iterate argument. Additionally, we are also able to say more for semirelativistic Schrödinger equation with general power-type nonlinearity.