{"title":"RN$\\mathbb {R}^N$ 中埃里克森-莱斯利问题弧上的局部和全局解","authors":"Daniele Barbera, Vladimir Georgiev","doi":"10.1002/mana.202300253","DOIUrl":null,"url":null,"abstract":"<p>The work deals with the Ericksen–Leslie system for nematic liquid crystals on the space <span></span><math>\n <semantics>\n <msup>\n <mi>R</mi>\n <mi>N</mi>\n </msup>\n <annotation>$\\mathbb {R}^N$</annotation>\n </semantics></math> with <span></span><math>\n <semantics>\n <mrow>\n <mi>N</mi>\n <mo>≥</mo>\n <mn>3</mn>\n </mrow>\n <annotation>$N\\ge 3$</annotation>\n </semantics></math>. In our work, we suppose the initial condition <span></span><math>\n <semantics>\n <msub>\n <mi>v</mi>\n <mn>0</mn>\n </msub>\n <annotation>$v_0$</annotation>\n </semantics></math> stays on an arc connecting two fixed orthogonal vectors on the unit sphere. Thanks to this geometric assumption, we prove through energy a priori estimates the local existence and the global existence for small initial data of a solution\n\n </p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Local and global solutions on arcs for the Ericksen–Leslie problem in \\n \\n \\n R\\n N\\n \\n $\\\\mathbb {R}^N$\",\"authors\":\"Daniele Barbera, Vladimir Georgiev\",\"doi\":\"10.1002/mana.202300253\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The work deals with the Ericksen–Leslie system for nematic liquid crystals on the space <span></span><math>\\n <semantics>\\n <msup>\\n <mi>R</mi>\\n <mi>N</mi>\\n </msup>\\n <annotation>$\\\\mathbb {R}^N$</annotation>\\n </semantics></math> with <span></span><math>\\n <semantics>\\n <mrow>\\n <mi>N</mi>\\n <mo>≥</mo>\\n <mn>3</mn>\\n </mrow>\\n <annotation>$N\\\\ge 3$</annotation>\\n </semantics></math>. In our work, we suppose the initial condition <span></span><math>\\n <semantics>\\n <msub>\\n <mi>v</mi>\\n <mn>0</mn>\\n </msub>\\n <annotation>$v_0$</annotation>\\n </semantics></math> stays on an arc connecting two fixed orthogonal vectors on the unit sphere. Thanks to this geometric assumption, we prove through energy a priori estimates the local existence and the global existence for small initial data of a solution\\n\\n </p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-07-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/mana.202300253\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mana.202300253","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Local and global solutions on arcs for the Ericksen–Leslie problem in
R
N
$\mathbb {R}^N$
The work deals with the Ericksen–Leslie system for nematic liquid crystals on the space with . In our work, we suppose the initial condition stays on an arc connecting two fixed orthogonal vectors on the unit sphere. Thanks to this geometric assumption, we prove through energy a priori estimates the local existence and the global existence for small initial data of a solution
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