Mass concentration for nonlinear Schrodinger equation with partial confinement

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:481

Article

Pan, Jingjing¹  Zhang, Jian¹ 

[1] Univ Elect Sci & Technol China, Sch Math Sci, Chengdu 611731, Sichuan, Peoples R China

关键词: Nonlinear Schrodinger equation;    Partial confinement;    Blow-up solution;    Mass concentration;    Variational characteristic;   

DOI  :  10.1016/j.jmaa.2019.123484

来源: Elsevier

【 摘 要 】

This paper studies the dynamical properties of blow-up solutions for nonlinear Schrodinger equation with partial confinement, which may model the Bose-Einstein condensate under a partial trap potential. By using the variational characteristic of the classic nonlinear scalar field equation and the Hamilton conservations, we first get the threshold for global existence and blow-up of the Cauchy problem on mass in two-dimensional space. Then, in terms of the refined compactness Lemma and the variational characteristic of the ground state of nonlinear scalar field equation, we get mass concentration properties of the blow-up solutions as well as limiting profile of the blow-up solutions with small super-critical mass. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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