$$B_{p,1}^{1}\cap C^{0,1}$$ 中的卡马萨-霍尔姆方程的失摆问题

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-08-02 DOI:10.1007/s13324-024-00956-5

Jinlu Li, Yanghai Yu, Yingying Guo, Weipeng Zhu

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引用次数: 0

摘要

本文研究了实线上卡马萨-霍姆方程的考奇问题。通过提出一种新的初始数据构造，我们证明了在$B_{p,1}^{1}\cap C^{0,1}$ with $p\in (2,\infty ]$ 的较小空间中的解映射在原点是不连续的。更确切地说，在（B_{p,1}^{1}\cap C^{0,1}\）中的初始数据可以保证卡马萨-霍尔姆方程在（W^{1,p}\cap C^{0,1}\）中有一个唯一的局部解，然而，这个解是不稳定的，在（B_{p,1}^{1}\cap C^{0,1}\）中会有膨胀。

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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Ill-posedness for the Camassa–Holm equation in $B_{p,1}^{1}\cap C^{0,1}$

In this paper, we study the Cauchy problem for the Camassa–Holm equation on the real line. By presenting a new construction of initial data, we show that the solution map in the smaller space $B_{p,1}^{1}\cap C^{0,1}$ with $p\in (2,\infty ]$ is discontinuous at origin. More precisely, the initial data in $B_{p,1}^{1}\cap C^{0,1}$ can guarantee that the Camassa–Holm equation has a unique local solution in $W^{1,p}\cap C^{0,1}$, however, this solution is instable and can have an inflation in $B_{p,1}^{1}\cap C^{0,1}$.

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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.

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