{"title":"常电场中液晶非线性波动方程的整体解","authors":"Lin-jun Huang","doi":"10.1137/18S017557","DOIUrl":null,"url":null,"abstract":"We construct a global conservative weak solution to the Cauchy problem for the non-linear variational wave equation $v_{tt} - c(v)(c(v)v_x)_x + \\frac{1}{2}(v+v^3)= 0$ where $c(\\cdot)$ is any smooth function with uniformly positive bounded value. This wave equation is derived from a wave system modelling nematic liquid crystals in a constant electric field.","PeriodicalId":93373,"journal":{"name":"SIAM undergraduate research online","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2018-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Global Solution to a Non-linear Wave Equation of Liquid Crystal in the Constant Electric Field\",\"authors\":\"Lin-jun Huang\",\"doi\":\"10.1137/18S017557\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We construct a global conservative weak solution to the Cauchy problem for the non-linear variational wave equation $v_{tt} - c(v)(c(v)v_x)_x + \\\\frac{1}{2}(v+v^3)= 0$ where $c(\\\\cdot)$ is any smooth function with uniformly positive bounded value. This wave equation is derived from a wave system modelling nematic liquid crystals in a constant electric field.\",\"PeriodicalId\":93373,\"journal\":{\"name\":\"SIAM undergraduate research online\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-06-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM undergraduate research online\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1137/18S017557\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM undergraduate research online","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1137/18S017557","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Global Solution to a Non-linear Wave Equation of Liquid Crystal in the Constant Electric Field
We construct a global conservative weak solution to the Cauchy problem for the non-linear variational wave equation $v_{tt} - c(v)(c(v)v_x)_x + \frac{1}{2}(v+v^3)= 0$ where $c(\cdot)$ is any smooth function with uniformly positive bounded value. This wave equation is derived from a wave system modelling nematic liquid crystals in a constant electric field.
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