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Article overview
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Scattering for a 3D cubic focusing nonlinear inhomogeneous NLS with a potential | | Qing Guo
; Hua Wang
; Xiaohua Yao
; | | Date: |
16 Jan 2018 | | Abstract: | In this paper, we consider the 3d cubic focusing inhomogeneous nonlinear
Schr"{o}dinger equation with a potential $$ iu_{t}+Delta
u-Vu+|x|^{-b}|u|^{2}u=0,;;(t,x) in {{f{R}} imes{f{R}}^{3}}, $$ where
$0<b<1$. We first establish global well-posedness and scattering for the radial
initial data $u_{0}$ in $H^{1}({f R}^{3})$ satisfying
$M(u_{0})^{1-s_{c}}E(u_{0})^{s_{c}}<mathcal{E}$ and
$|u_{0}|_{L^{2}}^{2(1-s_{c})}|H^{frac{1}{2}}u_{0}|_{L^{2}}^{2s_{c}}<mathcal{K}$
provided that $V$ is repulsive, where $mathcal{E}$ and $mathcal{K}$ are the
mass-energy and mass-kinetic of the ground state, respectively. Our result
extends the results of Hong cite{H} and Farah-Guzm$acute{
m a}$n cite{FG1}
with $bin(0,frac12)$ to the case $0<b<1$. | | Source: | arXiv, 1801.5165 | | Services: | Forum | Review | PDF | Favorites | |
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