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 $gamma>rac{3}{2}$ through a three-level approximation, energy estimates, and weakudconvergence 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.ud
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机译：本文研究了从复杂流体中选择的模型：液晶的可压缩流和不可压缩的流体-颗粒流。在液晶的可压缩流上，我们按照三元逼近，能量估计和弱超收敛方法建立了当γ> frac {3} {2} $时重新规范化的弱解的整体存在性。所谓的Lions-Feireisl方法。在不可压缩的流体粒子流上，我们建立了Leray弱解的整体存在性，该弱解是通过Galerkin方法，不动点参数和具有大量初始数据的收敛性分析构造的。唯一性是通过经典的Stokes方程理论和二维空间中的bootstrap参数建立的。 ud
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