{"title":"半空中稳定 p-Stokes 系统的利乌维尔式问题","authors":"","doi":"10.1016/j.jde.2024.09.014","DOIUrl":null,"url":null,"abstract":"<div><p>We study the Liouville problem for the steady <em>p</em>-Stokes system in the half-space. We prove that a bounded weak solution of the <em>p</em>-Stokes system with <span><math><mi>p</mi><mo>></mo><mn>1</mn></math></span> vanishes in two dimensions. For the three dimensional case, the same result is concluded, provided that <span><math><mi>p</mi><mo>></mo><mfrac><mrow><mn>5</mn></mrow><mrow><mn>3</mn></mrow></mfrac></math></span>.</p></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":2.4000,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Liouville type problem for the steady p-Stokes system in the half-space\",\"authors\":\"\",\"doi\":\"10.1016/j.jde.2024.09.014\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We study the Liouville problem for the steady <em>p</em>-Stokes system in the half-space. We prove that a bounded weak solution of the <em>p</em>-Stokes system with <span><math><mi>p</mi><mo>></mo><mn>1</mn></math></span> vanishes in two dimensions. For the three dimensional case, the same result is concluded, provided that <span><math><mi>p</mi><mo>></mo><mfrac><mrow><mn>5</mn></mrow><mrow><mn>3</mn></mrow></mfrac></math></span>.</p></div>\",\"PeriodicalId\":15623,\"journal\":{\"name\":\"Journal of Differential Equations\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.4000,\"publicationDate\":\"2024-09-12\",\"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/S002203962400593X\",\"RegionNum\":2,\"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":"Journal of Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S002203962400593X","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Liouville type problem for the steady p-Stokes system in the half-space
We study the Liouville problem for the steady p-Stokes system in the half-space. We prove that a bounded weak solution of the p-Stokes system with vanishes in two dimensions. For the three dimensional case, the same result is concluded, provided that .
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
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