English

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 R×T\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.

Keywords

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