{"title":"A free boundary inviscid model of flow-structure interaction","authors":"Igor Kukavica , Amjad Tuffaha","doi":"10.1016/j.jde.2024.08.045","DOIUrl":null,"url":null,"abstract":"<div><p>We obtain the local existence and uniqueness for a system describing interaction of an incompressible inviscid fluid, modeled by the Euler equations, and an elastic plate, represented by the fourth-order hyperbolic PDE. We provide a priori estimates for the existence with the optimal regularity <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>r</mi></mrow></msup></math></span>, for <span><math><mi>r</mi><mo>></mo><mn>2.5</mn></math></span>, on the fluid initial data and construct a unique solution of the system for initial data <span><math><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msup><mrow><mi>H</mi></mrow><mrow><mi>r</mi></mrow></msup></math></span> for <span><math><mi>r</mi><mo>≥</mo><mn>3</mn></math></span>. An important feature of the existence theorem is that the Taylor-Rayleigh instability does not occur. This is in contrast to the free-boundary Euler problem, where the stability condition on the initial pressure needs to be imposed.</p></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":2.4000,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022039624005278","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We obtain the local existence and uniqueness for a system describing interaction of an incompressible inviscid fluid, modeled by the Euler equations, and an elastic plate, represented by the fourth-order hyperbolic PDE. We provide a priori estimates for the existence with the optimal regularity , for , on the fluid initial data and construct a unique solution of the system for initial data for . An important feature of the existence theorem is that the Taylor-Rayleigh instability does not occur. This is in contrast to the free-boundary Euler problem, where the stability condition on the initial pressure needs to be imposed.
期刊介绍:
The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools.
Research Areas Include:
• Mathematical control theory
• Ordinary differential equations
• Partial differential equations
• Stochastic differential equations
• Topological dynamics
• Related topics