{"title":"无阻尼无粘性自由表面流体结构问题的全局时域弱解","authors":"Thomas Alazard, Igor Kukavica, Amjad Tuffaha","doi":"10.1007/s40818-025-00207-1","DOIUrl":null,"url":null,"abstract":"<div><p>We consider the Cauchy problem for an inviscid irrotational fluid on a domain with a free boundary governed by a fourth order linear elasticity equation. We first derive the Craig-Sulem-Zakharov formulation of the problem and then establish the existence of a global weak solution in two space dimensions for the fluid, in the general case without a damping term, for any initial data with finite energy.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"11 1","pages":""},"PeriodicalIF":2.4000,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Global-in-Time Weak Solutions for an Inviscid Free Surface Fluid-Structure Problem Without Damping\",\"authors\":\"Thomas Alazard, Igor Kukavica, Amjad Tuffaha\",\"doi\":\"10.1007/s40818-025-00207-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We consider the Cauchy problem for an inviscid irrotational fluid on a domain with a free boundary governed by a fourth order linear elasticity equation. We first derive the Craig-Sulem-Zakharov formulation of the problem and then establish the existence of a global weak solution in two space dimensions for the fluid, in the general case without a damping term, for any initial data with finite energy.</p></div>\",\"PeriodicalId\":36382,\"journal\":{\"name\":\"Annals of Pde\",\"volume\":\"11 1\",\"pages\":\"\"},\"PeriodicalIF\":2.4000,\"publicationDate\":\"2025-05-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Pde\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40818-025-00207-1\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Pde","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s40818-025-00207-1","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Global-in-Time Weak Solutions for an Inviscid Free Surface Fluid-Structure Problem Without Damping
We consider the Cauchy problem for an inviscid irrotational fluid on a domain with a free boundary governed by a fourth order linear elasticity equation. We first derive the Craig-Sulem-Zakharov formulation of the problem and then establish the existence of a global weak solution in two space dimensions for the fluid, in the general case without a damping term, for any initial data with finite energy.
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