Sharp threshold of global existence for nonlinear Schrödinger equation with partial confinement. (July 2020)

• Record Type: Journal Article
• Authors: Zhang, Jian
• Is Part Of: Nonlinear analysis. Volume 196(2020)
• Publication Date: 2020-07
• Subjects: 35B33 -- 35B35 -- 35Q55 -- 82D99; Nonlinear Schrödinger equation -- Partial confinement -- Bose–Einstein condensate -- Global existence -- Sharp threshold; 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.2020.111832
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This paper deals with the nonlinear Schrödinger equation with partial confinement, which may model the attractive Bose–Einstein condensate under a partial trap potential. By using the variational characteristic of the classic nonlinear scalar field equation and the Hamilton conservation, we get the threshold for global existence of the Cauchy problem on mass. Moreover by a novel scaling argument, we prove that this threshold is sharp. In addition, by a numerical computation, we obtain the numerical result of the threshold.