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arXiv · 2604.25593

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

Puti Dai·Zihua Guo
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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}.

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Puti Dai, Zihua Guo. 2026-04-28. Sharp Strichartz estimate for the 1D periodic Schr\"odinger equation. https://arxiv.org/abs/2604.25593

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