{"title":"Periodic Capillary-Gravity Water Waves of Small Amplitude","authors":"Qixiang Li, JinRong Wang","doi":"10.1007/s00021-024-00858-3","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we investigate two-dimensional capillary-gravity water waves of small amplitude, which propagate over a flat bed. We prove the existence of a local curve of solutions by using the Crandall–Rabinowitz local bifurcation theory, and show the uniqueness for the capillary-gravity water waves. Furthermore, we recover the dispersion relation for the constant vorticity setting. Moreover, we present a formal stability result for the bifurcation of the laminar solution. In addition, we prove the analyticity of the free surface.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 2","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Fluid Mechanics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00021-024-00858-3","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we investigate two-dimensional capillary-gravity water waves of small amplitude, which propagate over a flat bed. We prove the existence of a local curve of solutions by using the Crandall–Rabinowitz local bifurcation theory, and show the uniqueness for the capillary-gravity water waves. Furthermore, we recover the dispersion relation for the constant vorticity setting. Moreover, we present a formal stability result for the bifurcation of the laminar solution. In addition, we prove the analyticity of the free surface.
期刊介绍：
The Journal of Mathematical Fluid Mechanics (JMFM)is a forum for the publication of high-quality peer-reviewed papers on the mathematical theory of fluid mechanics, with special regards to the Navier-Stokes equations. As an important part of that, the journal encourages papers dealing with mathematical aspects of computational theory, as well as with applications in science and engineering. The journal also publishes in related areas of mathematics that have a direct bearing on the mathematical theory of fluid mechanics. All papers will be characterized by originality and mathematical rigor. For a paper to be accepted, it is not enough that it contains original results. In fact, results should be highly relevant to the mathematical theory of fluid mechanics, and meet a wide readership.
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