Continuum limit of fourth-order Schrödinger equations on the lattice
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915112552497152 |
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| author | Cheng, Jiawei Hua, Bobo |
| author_facet | Cheng, Jiawei Hua, Bobo |
| contents | In this paper, we consider the discrete fourth-order Schrödinger equation on the lattice $h\mathbb{Z}^2$. Uniform Strichartz estimates are established by analyzing frequency localized oscillatory integrals with the method of stationary phase and applying Littlewood-Paley inequalities. As an application, we obtain the precise rate of $L^2$ convergence from the solutions of discrete semilinear equations to those of the corresponding equations on the Euclidean plane $\mathbb{R}^2$ in the contimuum limit $h \rightarrow 0$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_11661 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Continuum limit of fourth-order Schrödinger equations on the lattice Cheng, Jiawei Hua, Bobo Analysis of PDEs In this paper, we consider the discrete fourth-order Schrödinger equation on the lattice $h\mathbb{Z}^2$. Uniform Strichartz estimates are established by analyzing frequency localized oscillatory integrals with the method of stationary phase and applying Littlewood-Paley inequalities. As an application, we obtain the precise rate of $L^2$ convergence from the solutions of discrete semilinear equations to those of the corresponding equations on the Euclidean plane $\mathbb{R}^2$ in the contimuum limit $h \rightarrow 0$. |
| title | Continuum limit of fourth-order Schrödinger equations on the lattice |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2501.11661 |