@Article{ATA-35-205, author = {}, title = {The Intercritical Defocusing Nonlinear Schrödinger Equations with Radial Initial Data in Dimensions Four and Higher}, journal = {Analysis in Theory and Applications}, year = {2019}, volume = {35}, number = {2}, pages = {205--234}, abstract = {

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.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-0006}, url = {http://global-sci.org/intro/article_detail/ata/13114.html} }