{"title":"Well-posedness and analyticity of solutions for the sixth-order Boussinesq equation","authors":"Amin Esfahani, Achenef Tesfahun","doi":"10.1142/s0219199724500056","DOIUrl":null,"url":null,"abstract":"<p>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 <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi mathvariant=\"normal\">Δ</mi><mi>u</mi></math></span><span></span> 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.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s0219199724500056","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
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 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.
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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