On strong dynamics of compressible nematic liquid crystals

Katharina Schade, Yoshihiro Shibata

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    7 Citations (Scopus)

    Abstract

    Given a uniform W3-1/q q -domain ω ⊆ ℝN for N q ∞, we consider a simplified Ericksen.Leslie system modeling the flow of compressible nematic liquid crystals based on Lin and Liu [Comm. Pure Appl. Math., 48 (1995), pp. 501.537]. We show the unique existence of local-intime strong solutions. Furthermore, if ω is bounded and initial data are chosen suitably small, we obtain global-in-time strong solutions. Our approach is based on maximal regularity estimates of the compressible Navier.Stokes equation by Enomoto, von Below, and Shibata [Ann. Univ. Ferrara, 60 (2014), pp. 55.89] and maximal regularity estimates for the Neumann problem as a consequence of Weis-fs 2001 vector-valued Fourier multiplier theorem.

    Original languageEnglish
    Pages (from-to)3963-3992
    Number of pages30
    JournalSIAM Journal on Mathematical Analysis
    Volume47
    Issue number5
    DOIs
    Publication statusPublished - 2015

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    Keywords

    • Compressible viscous fluid
    • Global solutions
    • Nematic liquid crystals
    • Quasi-linear parabolic evolution equations
    • Regularity

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics
    • Computational Mathematics

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