Global weak solution and blow-up criterion of the general Ericksen-Leslie system for nematic liquid crystal flows
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Publication:389920
DOI10.1016/J.JDE.2013.03.009zbMATH Open1282.35087arXiv1212.0043OpenAlexW2125103790MaRDI QIDQ389920
Author name not available (Why is that?)
Publication date: 22 January 2014
Published in: (Search for Journal in Brave)
Abstract: In this paper we investigate the three dimensional general Ericksen-Leslie (E--L) system with Ginzburg-Landau type approximation modeling nematic liquid crystal flows. First, by overcoming the difficulties from lack of maximum principle for the director equation and high order nonlinearities for the stress tensor, we prove existence of global-in-time weak solutions under physically meaningful boundary conditions and suitable assumptions on the Leslie coefficients, which ensures that the total energy of the E--L system is dissipated. Moreover, for the E--L system with periodic boundary conditions, we prove the local well-posedness of classical solutions under the so-called Parodi's relation and establish a blow-up criterion in terms of the temporal integral of both the maximum norm of the curl of the velocity field and the maximum norm of the gradient of the liquid crystal director field.
Full work available at URL: https://arxiv.org/abs/1212.0043
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