Initial-boundary value problems for poiseuille flow of nematic liquid crystal via full ericksen-leslie model

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 Ho"\lder continuous solution, which may include cusp singularity, for initial-boundary value problems with different types of boundary conditions.