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arXiv · 2501.11661

Continuum limit of fourth-order Schr\"{o}dinger equations on the lattice

Jiawei Cheng·Bobo Hua
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Abstract

In this paper, we consider the discrete fourth-order Schr\"{o}dinger 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 $h \rightarrow 0$.

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Jiawei Cheng, Bobo Hua. 2025-01-20. Continuum limit of fourth-order Schr\"{o}dinger equations on the lattice. https://arxiv.org/abs/2501.11661

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