The Intercritical Defocusing Nonlinear Schrödinger Equations with Radial Initial Data in Dimensions Four and Higher
Year: 2019
Analysis in Theory and Applications, Vol. 35 (2019), Iss. 2 : pp. 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.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.OA-0006
Analysis in Theory and Applications, Vol. 35 (2019), Iss. 2 : pp. 205–234
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 30
Keywords: Nonlinear Schrödinger equation scattering frequency-localized Morawetz estimate weighted Strichartz space.