{"title":"A two-component nonlinear variational wave system","authors":"Peder Aursand, Anders Nordli","doi":"10.1142/s0219891623500182","DOIUrl":null,"url":null,"abstract":"We derive a novel two-component generalization of the nonlinear variational wave equation as a model for the director field of a nematic liquid crystal with a variable order parameter. The equation admits classical solutions locally in time. We prove that a special semilinear case is globally well-posed. We show that a particular long time asymptotic expansion around a constant state in a moving frame satisfies the two-component Hunter–Saxton system.","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":"70 1","pages":"0"},"PeriodicalIF":0.5000,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Hyperbolic Differential Equations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0219891623500182","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
We derive a novel two-component generalization of the nonlinear variational wave equation as a model for the director field of a nematic liquid crystal with a variable order parameter. The equation admits classical solutions locally in time. We prove that a special semilinear case is globally well-posed. We show that a particular long time asymptotic expansion around a constant state in a moving frame satisfies the two-component Hunter–Saxton system.
期刊介绍：
This journal publishes original research papers on nonlinear hyperbolic problems and related topics, of mathematical and/or physical interest. Specifically, it invites papers on the theory and numerical analysis of hyperbolic conservation laws and of hyperbolic partial differential equations arising in mathematical physics. The Journal welcomes contributions in:
Theory of nonlinear hyperbolic systems of conservation laws, addressing the issues of well-posedness and qualitative behavior of solutions, in one or several space dimensions.
Hyperbolic differential equations of mathematical physics, such as the Einstein equations of general relativity, Dirac equations, Maxwell equations, relativistic fluid models, etc.
Lorentzian geometry, particularly global geometric and causal theoretic aspects of spacetimes satisfying the Einstein equations.
Nonlinear hyperbolic systems arising in continuum physics such as: hyperbolic models of fluid dynamics, mixed models of transonic flows, etc.
General problems that are dominated (but not exclusively driven) by finite speed phenomena, such as dissipative and dispersive perturbations of hyperbolic systems, and models from statistical mechanics and other probabilistic models relevant to the derivation of fluid dynamical equations.
Convergence analysis of numerical methods for hyperbolic equations: finite difference schemes, finite volumes schemes, etc.
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