TY - JOUR
T1 - The Blow-up Dynamics for the $L^2$-Critical Hartree Equation with Harmonic Potential
AU - Zhang , Mao
AU - Pan , Jingjing
AU - Zhang , Jian
JO - Journal of Nonlinear Modeling and Analysis
VL - 3
SP - 589
EP - 601
PY - 2024
DA - 2024/08
SN - 6
DO - http://doi.org/10.12150/jnma.2024.589
UR - https://global-sci.org/intro/article_detail/jnma/23350.html
KW - Hartree equation, harmonic potential, blow-up rate, upper bound,
mass concentration.
AB - <p style="text-align: justify;">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 $\mathbb{R}^N.$</p>