{"title":"有限通道中非常密度二维非齐次欧拉方程单调剪切流的无粘阻尼","authors":"Weiren Zhao","doi":"10.1007/s40818-025-00197-0","DOIUrl":null,"url":null,"abstract":"<div><p>We prove the nonlinear inviscid damping for a class of monotone shear flows with non-constant background density for the two-dimensional ideal inhomogeneous fluids in <span>\\(\\mathbb {T}\\times [0,1]\\)</span> when the initial perturbation is in Gevrey-<span>\\(\\frac{1}{s}\\)</span> (<span>\\(\\frac{1}{2}<s<1\\)</span>) class with compact support.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"11 1","pages":""},"PeriodicalIF":2.4000,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Inviscid Damping of Monotone Shear Flows for 2D Inhomogeneous Euler Equation with Non-Constant Density in a Finite Channel\",\"authors\":\"Weiren Zhao\",\"doi\":\"10.1007/s40818-025-00197-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We prove the nonlinear inviscid damping for a class of monotone shear flows with non-constant background density for the two-dimensional ideal inhomogeneous fluids in <span>\\\\(\\\\mathbb {T}\\\\times [0,1]\\\\)</span> when the initial perturbation is in Gevrey-<span>\\\\(\\\\frac{1}{s}\\\\)</span> (<span>\\\\(\\\\frac{1}{2}<s<1\\\\)</span>) class with compact support.</p></div>\",\"PeriodicalId\":36382,\"journal\":{\"name\":\"Annals of Pde\",\"volume\":\"11 1\",\"pages\":\"\"},\"PeriodicalIF\":2.4000,\"publicationDate\":\"2025-01-31\",\"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/s40818-025-00197-0\",\"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/s40818-025-00197-0","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Inviscid Damping of Monotone Shear Flows for 2D Inhomogeneous Euler Equation with Non-Constant Density in a Finite Channel
We prove the nonlinear inviscid damping for a class of monotone shear flows with non-constant background density for the two-dimensional ideal inhomogeneous fluids in \(\mathbb {T}\times [0,1]\) when the initial perturbation is in Gevrey-\(\frac{1}{s}\) (\(\frac{1}{2}<s<1\)) class with compact support.
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