晶格上四阶Schrödinger方程的连续统极限

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2025-07-29 DOI:10.1112/jlms.70247

Jiawei Cheng, Bobo Hua

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引用次数: 0

摘要

本文考虑晶格h z2 $h\mathbb {Z}^2$上的离散四阶Schrödinger方程。用定相法分析频率局域振荡积分，应用Littlewood-Paley不等式，建立了均匀的Strichartz估计。作为一个应用程序，在连续统极限h→0下，得到了离散半线性方程的解在欧几里得平面R 2$ \mathbb {R}^2$上收敛到相应方程的解的精确速率$h \右转0$。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Continuum limit of fourth-order Schrödinger equations on the lattice

In this paper, we consider the discrete fourth-order Schrödinger equation on the lattice $h Z^{2}$ . 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 $R^{2}$ in the continuum limit $h \to 0$ .

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来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.