@article{Cai2024, 
author = {Meixia Cai and Hui Jian and Min Gong},
title = {Global existence, blow-up and stability of standing waves for the Schrödinger-Choquard equation with harmonic potential},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {1},
pages = {495-520},
keywords = {Schrödinger-Choquard equation, harmonic potential, global existence, blow-up, orbital stability},
url = {https://www.sciopen.com/article/10.3934/math.2024027},
doi = {10.3934/math.2024027},
abstract = {In this article, we conduct a comprehensive investigation into the global existence, blow-up and stability of standing waves for a        L          2      -critical Schrödinger-Choquard equation with harmonic potential. First, by taking advantage of the ground-state solutions and scaling techniques, we obtain some criteria for the global existence and blow-up of the solutions. Second, in terms of the refined compactness argument, scaling techniques and the variational characterization of the ground state solution to the Choquard equation with        p          2        =  1  +            2      +      α        N  , we explore the limiting dynamics of blow-up solutions to the        L          2      -critical Choquard equation with        L          2      -subcritical perturbation, including the        L          2      -mass concentration and blow-up rate. Finally, the orbital stability of standing waves is investigated in the presence of        L          2      -subcritical perturbation, focusing        L          2      -critical perturbation and defocusing        L          2      -supercritical perturbation by using variational methods. Our results supplement the conclusions of some known works.}
}