Bilinear estimate for Schr\"odinger equation on $\mathbb{R} \times \mathbb{T}

We continue our study of bilinear estimates on waveguide $\mathbb{R}\times \mathbb{T}$ started in \cite{DFYZZ2024,Deng2023}. The main point of the current article is, comparing to previous work \cite{Deng2023}, that we obtain estimates beyond the semiclassical time regime. Our estimate is sharp in t...

Full description

Saved in:
Bibliographic Details
Main Authors Deng, Yangkendi, Di, Boning, Fan, Chenjie, Zhao, Zehua
Format Journal Article
LanguageEnglish
Published 08.07.2024
Subjects
Mathematics - Analysis of PDEs
Mathematics - Classical Analysis and ODEs
Online AccessGet full text

Cover

More Information
Summary:We continue our study of bilinear estimates on waveguide $\mathbb{R}\times \mathbb{T}$ started in \cite{DFYZZ2024,Deng2023}. The main point of the current article is, comparing to previous work \cite{Deng2023}, that we obtain estimates beyond the semiclassical time regime. Our estimate is sharp in the sense that one can construct examples which saturate this estimate.
DOI:10.48550/arxiv.2407.05654