English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

In the article, we prove the large data scattering for two problems, i.e. thedefocusing quintic nonlinear Schr{\"o}dinger equation on $\mathbb{R}^2$$\times$ $\mathbb{T}$ and the defocusing cubic nonlinear Schr{\"o}dingerequation on $\mathbb{R}^3$ $\times$ $\mathbb{T}$. Both of the two equations aremass supercritical and energy critical. The main ingredients of the proofscontain global Stricharz estimate, profile decomposition and energy inductionmethod. This paper is the second project of our series work (two papers,together with [36]) on large data scattering for the defocusing critical NLSwith integer index nonlinearity on low dimensional waveguides. At this point,that type of problems are almost solved except for two remaining resonantsystem conjectures and the quintic NLS problem on $\mathbb{R}\times\mathbb{T}$.

On scattering for the defocusing nonlinear Schr\"odinger equation on waveguide $ \mathbb{R}^m$ $\times$ $\mathbb{T}$ (when $m=2,3$)