Blow-up Analysis for the ${\varvec{ab}}$-Family of Equations

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-02-24 DOI:10.1007/s00021-024-00857-4

Wenguang Cheng, Ji Lin

引用次数: 0

Abstract

This paper investigates the Cauchy problem for the ab-family of equations with cubic nonlinearities, which contains the integrable modified Camassa–Holm equation ($a = \frac{1}{3}$, $b = 2$) and the Novikov equation ($a = 0$, $b = 3$) as two special cases. When $3a + b \ne 3$, the ab-family of equations does not possess the $H^1$-norm conservation law. We give the local well-posedness results of this Cauchy problem in Besov spaces and Sobolev spaces. Furthermore, we provide a blow-up criterion, the precise blow-up scenario and a sufficient condition on the initial data for the blow-up of strong solutions to the ab-family of equations. Our blow-up analysis does not rely on the use of the conservation laws.

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$${{varvec{ab}}$ -方程组的炸毁分析

本文研究了具有立方非线性的ab族方程的考奇问题，其中包含可积分的修正卡马萨-霍尔姆方程（（a = \frac{1}{3}\ ），（b = 2\ ））和诺维科夫方程（（a = 0\ ），（b = 3\ ））这两个特例。当 $3a + b \ne 3$ 时，ab-family方程不具备 $H^1$-norm 守恒定律。我们给出了这个 Cauchy 问题在 Besov 空间和 Sobolev 空间中的局部好求结果。此外，我们还提供了炸毁准则、精确的炸毁情形以及炸毁该 ab-family方程组强解的初始数据的充分条件。我们的炸毁分析并不依赖于守恒定律的使用。

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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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.

Blow-up Analysis for the \({\varvec{ab}}\)-Family of Equations

Abstract