Strichartz estimate for discrete Schrödinger equation on layered King's grid
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911081330376704 |
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| author | Wan, Zhiqiang Zhang, Heng |
| author_facet | Wan, Zhiqiang Zhang, Heng |
| contents | We establish the sharp \( l^1 \to l^{\infty} \) decay estimate for the discrete Schrödinger equation (DS) on the Layered King's Grid (LKG), with a dispersive decay rate of \( \langle t \rangle^{-13/12} \), which is faster than that for $3$-dimensional lattice (\( \langle t \rangle^{-1} \), see \cite{SK05}). This decay estimate enables us to derive the corresponding Strichartz estimate via the standard Keel--Tao argument. Our approach relies on using techniques from Newton polyhedra to analyze singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_20142 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strichartz estimate for discrete Schrödinger equation on layered King's grid Wan, Zhiqiang Zhang, Heng Analysis of PDEs Combinatorics We establish the sharp \( l^1 \to l^{\infty} \) decay estimate for the discrete Schrödinger equation (DS) on the Layered King's Grid (LKG), with a dispersive decay rate of \( \langle t \rangle^{-13/12} \), which is faster than that for $3$-dimensional lattice (\( \langle t \rangle^{-1} \), see \cite{SK05}). This decay estimate enables us to derive the corresponding Strichartz estimate via the standard Keel--Tao argument. Our approach relies on using techniques from Newton polyhedra to analyze singularities. |
| title | Strichartz estimate for discrete Schrödinger equation on layered King's grid |
| topic | Analysis of PDEs Combinatorics |
| url | https://arxiv.org/abs/2507.20142 |