{"title":"类lipschitz域二维非自治不可压缩流体流动的适定性","authors":"Xin-Guang Yang and Shubin Wang sci","doi":"10.4208/JPDE.V32.N1.6","DOIUrl":null,"url":null,"abstract":"This paper is concerned with the global well-posedness and regularity of weak solutions for the 2D non-autonomous incompressible Navier-Stokes equation with a inhomogeneous boundary condition in Lipschitz-like domain. Using the estimate for governing steady state equation and Hardy’s inequality, the existence and regularity of global unique weak solution can be proved. Moreover, these results also hold for 2D Navier-Stokes equation with Rayleigh’s friction and Navier-Stokes-Voigt flow, but invalid for three dimension. AMS Subject Classifications: 35B40, 35B41, 35Q30, 76D03, 76D05 Chinese Library Classifications: O175.27","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":"289 1","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Well-Posedness for the 2D Non-Autonomous Incompressible Fluid Flow in Lipschitz-like Domain\",\"authors\":\"Xin-Guang Yang and Shubin Wang sci\",\"doi\":\"10.4208/JPDE.V32.N1.6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper is concerned with the global well-posedness and regularity of weak solutions for the 2D non-autonomous incompressible Navier-Stokes equation with a inhomogeneous boundary condition in Lipschitz-like domain. Using the estimate for governing steady state equation and Hardy’s inequality, the existence and regularity of global unique weak solution can be proved. Moreover, these results also hold for 2D Navier-Stokes equation with Rayleigh’s friction and Navier-Stokes-Voigt flow, but invalid for three dimension. AMS Subject Classifications: 35B40, 35B41, 35Q30, 76D03, 76D05 Chinese Library Classifications: O175.27\",\"PeriodicalId\":43504,\"journal\":{\"name\":\"Journal of Partial Differential Equations\",\"volume\":\"289 1\",\"pages\":\"\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2019-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Partial Differential Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4208/JPDE.V32.N1.6\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Partial Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4208/JPDE.V32.N1.6","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Well-Posedness for the 2D Non-Autonomous Incompressible Fluid Flow in Lipschitz-like Domain
This paper is concerned with the global well-posedness and regularity of weak solutions for the 2D non-autonomous incompressible Navier-Stokes equation with a inhomogeneous boundary condition in Lipschitz-like domain. Using the estimate for governing steady state equation and Hardy’s inequality, the existence and regularity of global unique weak solution can be proved. Moreover, these results also hold for 2D Navier-Stokes equation with Rayleigh’s friction and Navier-Stokes-Voigt flow, but invalid for three dimension. AMS Subject Classifications: 35B40, 35B41, 35Q30, 76D03, 76D05 Chinese Library Classifications: O175.27
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