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Global weak solution to the flow of liquid crystals system
Author(s) -
Jiang Fei,
Tan Zhong
Publication year - 2009
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1132
Subject(s) - bounded function , mathematics , domain (mathematical analysis) , flow (mathematics) , space (punctuation) , liquid crystal , weak solution , energy (signal processing) , mathematical analysis , pure mathematics , mathematical physics , physics , geometry , condensed matter physics , computer science , statistics , operating system
Abstract In this paper, we study a simplified system for the flow of nematic liquid crystals in a bounded domain in the three‐dimensional space. We derive the basic energy law which enables us to prove the global existence of the weak solutions under the condition that the initial density belongs to L γ (Ω) for any \documentclass{article}\footskip=0pc\pagestyle{empty}\begin{document}$\gamma >\frac{3}{2}$\end{document} . Especially, we also obtain that the weak solutions satisfy the energy inequality in integral or differential form. Copyright © 2009 John Wiley & Sons, Ltd.