{"title":"部分自由边界二维向列液晶流弱解的全局存在性","authors":"Yannick Sire, Yantao Wu, Yifu Zhou","doi":"10.1112/jlms.70008","DOIUrl":null,"url":null,"abstract":"<p>We consider a nematic liquid crystal flow with partially free boundary in a smooth bounded domain in <span></span><math>\n <semantics>\n <msup>\n <mi>R</mi>\n <mn>2</mn>\n </msup>\n <annotation>$\\mathbb {R}^2$</annotation>\n </semantics></math>. We prove regularity estimates and the global existence of weak solutions enjoying partial regularity properties, and a uniqueness result.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"110 5","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Global existence of weak solutions to the two-dimensional nematic liquid crystal flow with partially free boundary\",\"authors\":\"Yannick Sire, Yantao Wu, Yifu Zhou\",\"doi\":\"10.1112/jlms.70008\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We consider a nematic liquid crystal flow with partially free boundary in a smooth bounded domain in <span></span><math>\\n <semantics>\\n <msup>\\n <mi>R</mi>\\n <mn>2</mn>\\n </msup>\\n <annotation>$\\\\mathbb {R}^2$</annotation>\\n </semantics></math>. We prove regularity estimates and the global existence of weak solutions enjoying partial regularity properties, and a uniqueness result.</p>\",\"PeriodicalId\":49989,\"journal\":{\"name\":\"Journal of the London Mathematical Society-Second Series\",\"volume\":\"110 5\",\"pages\":\"\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-10-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the London Mathematical Society-Second Series\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/jlms.70008\",\"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 the London Mathematical Society-Second Series","FirstCategoryId":"100","ListUrlMain":"https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/jlms.70008","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
摘要
我们考虑了在 R 2 $\mathbb {R}^2$ 的光滑有界域中具有部分自由边界的向列液晶流。我们证明了正则性估计和具有部分正则性的弱解的全局存在性，以及唯一性结果。
Global existence of weak solutions to the two-dimensional nematic liquid crystal flow with partially free boundary
We consider a nematic liquid crystal flow with partially free boundary in a smooth bounded domain in . We prove regularity estimates and the global existence of weak solutions enjoying partial regularity properties, and a uniqueness result.
期刊介绍：
The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.
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