TY - JOUR
T1 - The Intercritical Defocusing Nonlinear Schrödinger Equations with Radial Initial Data in Dimensions Four and Higher
AU - Chuanwei Gao, Changxing Miao & Jianwei Yang-Urbain
JO - Analysis in Theory and Applications
VL - 2
SP - 205
EP - 234
PY - 2019
DA - 2019/04
SN - 35
DO - http://doi.org/10.4208/ata.OA-0006
UR - https://global-sci.org/intro/article_detail/ata/13114.html
KW - Nonlinear Schrödinger equation, scattering,  frequency-localized  Morawetz estimate, weighted Strichartz space.
AB - <p style="text-align: justify;">In this paper, we consider the defocusing nonlinear Schrödinger equation in space dimensions $d\geq 4$. We prove that if $u$ is a radial solution which is $priori$ bounded in the critical Sobolev space, that is, $u\in L_t^\infty \dot{H}^{s_c}_x$, then $u$ is global and scatters. In practice, we use weighted Strichartz space adapted for our setting which ultimately helps us solve the problems in cases $d\geq 4$ and $0&lt;s_c&lt;{1}/{2}$. The results in this paper extend the work of [27, Commun. PDEs, 40 (2015), 265-308] to higher dimensions.</p>