{"title":"A Sharp Version of the Benjamin and Lighthill Conjecture for Steady Waves with Vorticity","authors":"Evgeniy Lokharu","doi":"10.1007/s00021-024-00859-2","DOIUrl":null,"url":null,"abstract":"<div><p>We give a complete proof of the classical Benjamin and Lighthill conjecture for arbitrary two-dimensional steady water waves with vorticity. We show that the flow force constant of an arbitrary smooth solution is bounded by the flow force constants for the corresponding conjugate laminar flows. We prove these inequalities without any assumptions on the geometry of the surface profile and put no restrictions on the wave amplitude. Furthermore, we give a complete description of all cases when the equalities can occur. In particular, that excludes the existence of one-sided bores and multi-hump solitary waves. Our conclusions are new already for Stokes waves with a constant vorticity, while the case of equalities is new even in the classical setting of irrotational waves.</p></div>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-024-00859-2.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00021-024-00859-2","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
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Abstract
We give a complete proof of the classical Benjamin and Lighthill conjecture for arbitrary two-dimensional steady water waves with vorticity. We show that the flow force constant of an arbitrary smooth solution is bounded by the flow force constants for the corresponding conjugate laminar flows. We prove these inequalities without any assumptions on the geometry of the surface profile and put no restrictions on the wave amplitude. Furthermore, we give a complete description of all cases when the equalities can occur. In particular, that excludes the existence of one-sided bores and multi-hump solitary waves. Our conclusions are new already for Stokes waves with a constant vorticity, while the case of equalities is new even in the classical setting of irrotational waves.
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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