Dynamics of the nonlinear Hartree equation with a focusing and defocusing perturbation. (September 2022)

• Record Type: Journal Article
• Authors: Tian, Shuai; Zhu, Shihui
• Is Part Of: Nonlinear analysis. Volume 222(2022)
• Publication Date: 2022-09
• Subjects: Nonlinear Schrödinger equation -- Focusing and defocusing perturbation -- Refined compactness lemma -- Sharp energy threshold -- Limiting profile; 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.2022.112980
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we identify the sharp energy threshold for the global existence and blow-up to the Hartree equation with a focusing and defocusing perturbation, respectively, by utilizing comprehensive potential-well structures generated by the combined nonlinearities. Then, by adopting the refined compactness lemma, we detect the dynamical properties of blow-up solutions near the sharp threshold mass, including blow-up rate, concentration, weak limits and limiting profile decomposition of blow-up solutions with small super critical mass.