离散非线性薛定谔方程的索波列夫规范增长和强收敛性

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications Pub Date : 2024-02-20 DOI:10.1016/j.na.2024.113517

Quentin Chauleur

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引用次数: 0

摘要

我们展示了无限晶格上离散非线性薛定谔方程的解在任意索波列夫规范下向整个空间上非线性薛定谔方程的解的强收敛性。我们将注意力局限于一维和二维情况，参数集意味着连续方程的全局好求解性。我们的证明依赖于对香农插值的双线性估计以及对离散索波列夫规范增长的控制，我们都证明了这一点。

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Growth of Sobolev norms and strong convergence for the discrete nonlinear Schrödinger equation

We show the strong convergence in arbitrary Sobolev norms of solutions of the discrete nonlinear Schrödinger on an infinite lattice towards those of the nonlinear Schrödinger equation on the whole space. We restrict our attention to the one and two-dimensional case, with a set of parameters which implies global well-posedness for the continuous equation. Our proof relies on the use of bilinear estimates for the Shannon interpolation as well as the control of the growth of discrete Sobolev norms that we both prove.

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来源期刊

Nonlinear Analysis-Theory Methods & Applications 数学-数学

CiteScore

3.30

自引率

0.00%

发文量

265

审稿时长

60 days

期刊介绍： Nonlinear Analysis focuses on papers that address significant problems in Nonlinear Analysis that have a sustainable and important impact on the development of new directions in the theory as well as potential applications. Review articles on important topics in Nonlinear Analysis are welcome as well. In particular, only papers within the areas of specialization of the Editorial Board Members will be considered. Authors are encouraged to check the areas of expertise of the Editorial Board in order to decide whether or not their papers are appropriate for this journal. The journal aims to apply very high standards in accepting papers for publication.