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.In this paper, we study the initial-boundary value problem for the Poiseuille flow of a hyperbolic-parabolic Ericksen–Leslie model of nematic liquid crystals in one space dimension. We consider a simplified system by restricting the Leslie coefficients to special cases such that some quantities are constants. Due to the quasilinearity, the solution of this model in general forms cusp singularity. We prove the global existence of a Hölder continuous solution, which may include cusp singularity, for initial-boundary value problems with different types of boundary conditions.Keywordsliquid crystalEricksen–LesliePoiseuille flowglobal existenceinitial-boundary value problemMSC codes35M3335L5376D03
Chen et al. (2024) studied this question.
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