On Strichartz estimates for many-body Schrödinger equation in the periodic setting
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| Format: | Preprint |
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2023
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| _version_ | 1866914670809448448 |
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| author | Huang, Xiaoqi Yu, Xueying Zhao, Zehua Zheng, Jiqiang |
| author_facet | Huang, Xiaoqi Yu, Xueying Zhao, Zehua Zheng, Jiqiang |
| contents | In this paper, we prove Strichartz estimates for many body Schrödinger equations in the periodic setting, specifically on tori $\mathbb{T}^d$, where $d\geq 3$. The results hold for both rational and irrational tori, and for small interacting potentials in a certain sense. Our work is based on the standard Strichartz estimate for Schrödinger operators on periodic domains, as developed in Bourgain-Demeter \cite{BD}. As a comparison, this result can be regarded as a periodic analogue of Hong \cite{hong2017strichartz} though we do not use the same perturbation method. We also note that the perturbation method fails due to the derivative loss property of the periodic Strichartz estimate. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2304_00882 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Strichartz estimates for many-body Schrödinger equation in the periodic setting Huang, Xiaoqi Yu, Xueying Zhao, Zehua Zheng, Jiqiang Analysis of PDEs In this paper, we prove Strichartz estimates for many body Schrödinger equations in the periodic setting, specifically on tori $\mathbb{T}^d$, where $d\geq 3$. The results hold for both rational and irrational tori, and for small interacting potentials in a certain sense. Our work is based on the standard Strichartz estimate for Schrödinger operators on periodic domains, as developed in Bourgain-Demeter \cite{BD}. As a comparison, this result can be regarded as a periodic analogue of Hong \cite{hong2017strichartz} though we do not use the same perturbation method. We also note that the perturbation method fails due to the derivative loss property of the periodic Strichartz estimate. |
| title | On Strichartz estimates for many-body Schrödinger equation in the periodic setting |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2304.00882 |