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 Plus annual

Presents the access of premium content as premium feature

Premium Content

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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we study the well-posedness theory and the scatteringasymptotics for fourth-order Schr\"odinger equations (4NLS) on waveguidemanifolds (semiperiodic spaces) $\mathbb{R}^d\times \mathbb{T}^n$, $d \geq 5$,$n=1,2,3$. The tori component $\mathbb{T}^n$ can be generalized to$n$-dimensional compact manifolds $\mathcal{M}^n$. First, we modify Strichartzestimates for 4NLS on waveguide manifolds, with which we establish thewell-posedness theory in proper function spaces via the standard contractionmapping method. Moreover, we prove the scattering asymptotics based on aninteraction Morawetz-type estimate established for 4NLS on waveguides. At last,we discuss the higher dimensional analogue, the focusing scenario and give somefurther remarks on this research line. This result can be regarded as thewaveguide analogue of Pausader \cite{Pau2,Pau1,Pau3} and the 4NLS analogue ofTzvetkov-Visciglia \cite{TV2}.

Global Well-posedness and scattering for fourth-order Schr\"odinger equations on waveguide manifolds