TY - JOUR T1 - The Intercritical Defocusing Nonlinear Schrödinger Equations with Radial Initial Data in Dimensions Four and Higher 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 -

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 $0<s_c<{1}/{2}$. The results in this paper extend the work of [27, Commun. PDEs, 40 (2015), 265-308] to higher dimensions.