论三维双曲空间上五元 NLS 的衰减特性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-06-27 DOI:10.1016/j.na.2024.113599

Chutian Ma , Han Wang , Xueying Yu , Zehua Zhao

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引用次数: 0

摘要

本文研究了五元 NLS 在三维双曲空间 H3 上的（点向）衰减特性。我们证明了非线性解享有与线性解相同的衰减率。这一结果基于 Ionescu 等人（2012）中相关的全局拟合和散射结果。这将（Fan 和 Zhao，2021 年）的欧几里得工作扩展到了双曲空间，并对正则性要求进行了额外改进（假定了较低和几乎临界的正则性）。意识到这种改进也适用于欧几里得情况，我们得到了 Yu 等人（2023 年）最近研究的四阶 NLS 类似结果，其正则性假设更好，即几乎临界。

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On the decaying property of quintic NLS on 3D hyperbolic space

In this paper, we study the (pointwise) decaying property of quintic NLS on the three-dimensional hyperbolic space $H^{3}$ . We show the nonlinear solution enjoys the same decay rate as the linear solution does. This result is based on the associated global well-posedness and scattering result in Ionescu et al. (2012). This extends (Fan and Zhao, 2021)’ Euclidean works to the hyperbolic space with additional improvements in regularity requirement (lower and almost critical regularity assumed). Realizing such improvements also work for the Euclidean case, we obtain a result for the fourth-order NLS analogue studied in Yu et al. (2023) recently with better, i.e. almost critical regularity assumption.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.