Local and global solutions on arcs for the Ericksen–Leslie problem in R N $\mathbb {R}^N$

Pub Date : 2024-07-29 DOI:10.1002/mana.202300253

Daniele Barbera, Vladimir Georgiev

{"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":"The work deals with the Ericksen–Leslie system for nematic liquid crystals on the space <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 <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 <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 ","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}

引用次数: 0

Abstract

The work deals with the Ericksen–Leslie system for nematic liquid crystals on the space $R^{N}$ with $N \geq 3$ . In our work, we suppose the initial condition $v_{0}$ 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

查看原文

RN$\mathbb {R}^N$ 中埃里克森-莱斯利问题弧上的局部和全局解

我们的研究涉及有......空间的向列液晶的埃里克森-莱斯利系统。在我们的研究中，我们假设初始条件停留在连接单位球面上两个固定正交向量的弧线上。得益于这一几何假设，我们通过能量先验估计证明了在小初始数据条件下，Ⅳ 的解的局部存在性和全局存在性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文