Well-posedness and analyticity of solutions for the sixth-order Boussinesq equation

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-02-16 DOI:10.1142/s0219199724500056

Amin Esfahani, Achenef Tesfahun

引用次数: 0

Abstract

In this paper, the sixth-order Boussinesq equation is studied. We extend the local well-posedness theory for this equation with quadratic and cubic nonlinearities to the high dimensional case. In spite of having the “bad” fourth term $Δ u$ in the equation, we derive some dispersive estimates leading to the existence of local solutions which also improves the previous results in the cubic case. In addition, we show persistence of spatial analyticity of solutions for the cubic nonlinearity.

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六阶布辛斯方程的良好求解和解析性

本文研究了六阶布辛斯方程。我们将该方程的二次方和三次方非线性的局部好求解理论扩展到高维情况。尽管方程中存在 "坏 "的第四项 Δu，我们仍推导出了一些分散估计值，从而得出了局部解的存在性，这也改进了之前三次方程的结果。此外，我们还展示了立方非线性解的空间解析性的持久性。

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.