Volume 35, Issue 2
The Intercritical Defocusing Nonlinear Schrödinger Equations with Radial Initial Data in Dimensions Four and Higher

Chuanwei Gao, Changxing Miao & Jianwei Yang-Urbain

Anal. Theory Appl., 35 (2019), pp. 205-234.

Published online: 2019-04

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  • 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.

  • Keywords

Nonlinear Schrödinger equation, scattering, frequency-localized Morawetz estimate, weighted Strichartz space.

  • AMS Subject Headings

35P25, 35Q55, 47J35

  • Copyright

COPYRIGHT: © Global Science Press

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@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} }
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.

Chuanwei Gao, Changxing Miao & Jianwei Yang-Urbain. (2019). The Intercritical Defocusing Nonlinear Schrödinger Equations with Radial Initial Data in Dimensions Four and Higher. Analysis in Theory and Applications. 35 (2). 205-234. doi:10.4208/ata.OA-0006
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