@article{Jian2023, 
author = {Hui Jian and Min Gong and Meixia Cai},
title = {Global existence, blow-up and mass concentration for the inhomogeneous nonlinear Schrödinger equation with inverse-square potential},
year = {2023},
journal = {Electronic Research Archive},
volume = {31},
number = {12},
pages = {7427-7451},
keywords = {inhomogeneous nonlinear Schrödinger equation, inverse-square potential, blow-up, global existence, mass concentration},
url = {https://www.sciopen.com/article/10.3934/era.2023375},
doi = {10.3934/era.2023375},
abstract = {In the current paper, the Cauchy problem for the inhomogeneous nonlinear Schrödinger equation including inverse-square potential is considered. First, some criteria of global existence and finite-time blow-up in the mass-critical and mass-supercritical settings with    0  <  c  ≤      c          ∗       are obtained. Then, by utilizing the potential well method and the sharp Sobolev constant, the sharp condition of blow-up is derived in the energy-critical case with    0  <  c  <                    N                  2                    +      4      N              (      N      +      2              )                  2                          c          ∗      . Finally, we establish the mass concentration property of explosive solutions, as well as the dynamic behaviors of the minimal-mass blow-up solutions in the        L          2      -critical setting for    0  <  c  <      c          ∗      , by means of the variational characterization of the ground-state solution to the elliptic equation, scaling techniques and a suitable refined compactness lemma. Our results generalize and supplement the ones of some previous works.}
}