Remarks on nonlinear Schrödinger equations arising on rotational Bose–Einstein condensates. (January 2022)

• Record Type: Journal Article
• Authors: Dinh, Van Duong
• Is Part Of: Nonlinear analysis. Volume 214(2022)
• Publication Date: 2022-01
• Subjects: 35A01 -- 35B44 -- 35Q55; Nonlinear Schrödinger equation -- Harmonic potential -- Global existence -- Blow-up -- Rotation; 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.2021.112587
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we study the Cauchy problem for nonlinear Schrödinger equations arising as an effective model of the Bose–Einstein condensate in a magnetic trap rotating with an angular velocity. We first establish sufficient conditions showing the existence of global-in-time and finite time blow-up solutions to the equation. We next derive sharp thresholds for global existence versus finite time blow-up in the mass-critical and mass-supercritical cases. We also study the existence and strong instability of ground state standing waves related to the equation. Finally we prove the existence, non-existence, and orbital stability of prescribed mass standing waves when the rotational speed is smaller than a critical value.