{Some Analytical Issues for the Selected Complex Fluids Models

In this dissertation, we study the selected models from complex fluids: compressible flow of liquid crystals and the incompressible fluid-particles flow. On the compressible flow of liquid crystals, we establish the global existence of renormalized weak solutions when $\gamma>\frac{3}{2}$ through a three-level approximation, energy estimates, and weak\ud convergence methods in the spirit of the so-called Lions-Feireisl method. On the incompressible fluid-particles flow, we establish the global existence of Leray weak solutions which was constructed by the Galerkin methods, fixed point arguments, and convergence analysis with the large initial data. The uniqueness was established by the classical theory of Stokes equations and a bootstrap argument in the two dimensional space.\u