On Decaying Properties of Nonlinear Schrödinger Equations

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Mathematical Analysis Pub Date : 2024-05-03 DOI:10.1137/23m1557544

Chenjie Fan, Gigliola Staffilani, Zehua Zhao

引用次数: 0

Abstract

SIAM Journal on Mathematical Analysis, Volume 56, Issue 3, Page 3082-3109, June 2024.
Abstract. In this paper we discuss quantitative (pointwise) decay estimates for solutions to the 3D cubic defocusing nonlinear Schrödinger equation with various (deterministic and random) initial data. We show that nonlinear solutions enjoy the same decay rate as the linear ones. The regularity assumption on the initial data is much lower than in previous results (see [C. Fan and Z. Zhao, Discrete Contin. Dyn. Syst., 41 (2021), pp. 3973–3984] and the references therein), and, moreover, we quantify the decay, which is another novelty of this work. Furthermore, we show that the (physical) randomization of the initial data can be used to replace the [math]-data assumption (see [C. Fan and Z. Zhao, Proc. Amer. Math. Soc., 151 (2023), pp. 2527–2542] for the necessity of the [math]-data assumption).

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论非线性薛定谔方程的衰变特性

SIAM 数学分析期刊》，第 56 卷，第 3 期，第 3082-3109 页，2024 年 6 月。摘要。本文讨论了具有各种（确定性和随机）初始数据的三维立方离焦非线性薛定谔方程解的定量（点式）衰减估计。我们证明，非线性解与线性解具有相同的衰减率。对初始数据的正则性假设比以前的结果（见 [C. Fan and Z. Zhao, Discrete Contin. Dyn. Syst.此外，我们还证明了初始数据的（物理）随机化可以用来取代[math]-data 假设（关于[math]-data 假设的必要性，请参见[C. Fan and Z. Zhao, Proc. Amer. Math. Soc., 151 (2023), pp.）

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来源期刊

SIAM Journal on Mathematical Analysis 数学-应用数学

CiteScore

3.30

自引率

5.00%

发文量

175

审稿时长

12 months

期刊介绍： SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena. Submission of a manuscript to a SIAM journal is representation by the author that the manuscript has not been published or submitted simultaneously for publication elsewhere. Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.