Year: 2024
Author: Mao Zhang, Jingjing Pan, Jian Zhang
Journal of Nonlinear Modeling and Analysis, Vol. 6 (2024), Iss. 3 : pp. 589–601
Abstract
In this paper, we study the $L^2$-critical Hartree equation with harmonic potential which arises in quantum theory of large system of nonrelativistic bosonic atoms and molecules. Firstly, by using the variational characteristic of the nonlinear elliptic equation and the Hamilton conservations, we get the sharp threshold for global existence and blow-up of the Cauchy problem. Then, in terms of a change of variables, we first find the relation between the Hartree equation with and without harmonic potential. Furthermore, we prove the upper bound of blow-up rate in $\mathbb{R}^3$ as well as the mass concentration of blow-up solution for the Hartree equation with harmonic potential in $\mathbb{R}^N.$
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2024.589
Journal of Nonlinear Modeling and Analysis, Vol. 6 (2024), Iss. 3 : pp. 589–601
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Hartree equation harmonic potential blow-up rate upper bound mass concentration.