Bilinear estimate for SchrÃ¶dinger equation on $\mathbb{R} \times \mathbb{T}$

Yangkendi Deng; Boning Di; Chenjie Fan; Zehua Zhao

doi:10.1016/j.jfa.2025.111312

paper

Bilinear estimate for SchrÃ¶dinger equation on $R \times T$

arXiv:2407.05654 · doi:10.1016/j.jfa.2025.111312

Abstract

We continue our study of bilinear estimates on waveguide $R \times T$ 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.

19 pages, comments are welcome

Bilinear estimate for SchrÃ¶dinger equation on R×T

Abstract

Bilinear estimate for SchrÃ¶dinger equation on $R \times T$