Bilinear estimate for Schr\"odinger equation on $\mathbb{R} \times \mathbb{T}$
Analysis of PDEs
2025-12-17 v1 Classical Analysis and ODEs
Abstract
We continue our study of bilinear estimates on waveguide 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.
Cite
@article{arxiv.2407.05654,
title = {Bilinear estimate for Schr\"odinger equation on $\mathbb{R} \times \mathbb{T}$},
author = {Yangkendi Deng and Boning Di and Chenjie Fan and Zehua Zhao},
journal= {arXiv preprint arXiv:2407.05654},
year = {2025}
}
Comments
19 pages, comments are welcome