Sharp Strichartz estimate for the 1D periodic Schr\"odinger equation

Puti Dai; Zihua Guo

Sharp Strichartz estimate for the 1D periodic Schr\"odinger equation

Analysis of PDEs 2026-05-05 v2 Classical Analysis and ODEs

Authors: Puti Dai , Zihua Guo

Abstract

We prove the following estimate $\|{e^{it\partial_x^2}f}\|_{L_{(t,x)\in \mathbb{T}^2}^6}\leq C (\log N)^{{1/6}} \|f\|_{L^2_x(\mathbb{T})},$ assuming $\mbox{supp} (\hat f)\subset [-N,N]$ for $N>1$ . The bound $(\log N)^{{1/6}}$ is sharp in view of the lower bound by Bourgain \cite{Bourgain}.

Keywords

schrödinger equation strichartz estimates

Cite

@article{arxiv.2604.25593,
  title  = {Sharp Strichartz estimate for the 1D periodic Schr\"odinger equation},
  author = {Puti Dai and Zihua Guo},
  journal= {arXiv preprint arXiv:2604.25593},
  year   = {2026}
}

Comments

There is a serious gap in the proof

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