Sharp Strichartz estimate for the 1D periodic Schrödinger equation
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913082375143424 |
|---|---|
| author | Dai, Puti Guo, Zihua |
| author_facet | Dai, Puti Guo, Zihua |
| contents | 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}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_25593 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sharp Strichartz estimate for the 1D periodic Schrödinger equation Dai, Puti Guo, Zihua Analysis of PDEs Classical Analysis and ODEs 42B37, 35Q41 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}. |
| title | Sharp Strichartz estimate for the 1D periodic Schrödinger equation |
| topic | Analysis of PDEs Classical Analysis and ODEs 42B37, 35Q41 |
| url | https://arxiv.org/abs/2604.25593 |