Bilinear estimate for Schrödinger equation on $\mathbb{R}\times \mathbb{T}$

Abstract

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.

arXiv comment19 pages, comments are welcome

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