Sharp conditions of global existence for nonlinear Schrödinger equation with a harmonic potential

Advances in Nonlinear Analysis

article

Mingyou Zhang¹  Md Salik Ahmed² 

[1] College of Science, Northwest A&F University;Department of Mathematics and Physics, North South University-1229

关键词: nonlinear Schrödinger equation;    harmonic potential;    potential wells;    global existence;    invariant sets;   

DOI  :  10.1515/anona-2020-0031

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

The Cauchy problem of nonlinear Schrödinger equation with a harmonic potential for describing the attractive Bose-Einstein condensate under the magnetic trap is considered. We give some sufficient conditions of global existence and finite time blow up of solutions by introducing a family of potential wells. Some different sharp conditions for global existence, and some invariant sets of solutions are also obtained here.

【 授权许可】

CC BY