本项目将在理论上研究变黏性的Navier-Stokes方程和几类可压复杂流体力学方程组在二维，三维空间中的全局解性态，以及薄膜边界各向异性所导致的有效边界条件。建立一些可压粘弹流体，液晶等流体模型；讨论有粘性状态下的blow-up机制；研究无粘状态下的奇性形成；讨论解对粘性系数的依赖状态，解的大时间性态并解决高维黏性依赖密度的等熵可压缩流体力学方程组的适定性问题.本项目将对可压的粘弹性流体方程组，MHD方程组等，在有粘性条件下讨论其blow-up的机制并讨论黏性依赖密度的可压Navier-Stokes方程组的适定性，而无粘条件下分析三维模型的奇性形成.并且对粘性系数依赖于密度及温度时，分别讨论其blow-up机制及奇性形成.还将研究不同薄膜区域各向异性粘性以及各向异性微观结构所引起的宏观有效边界条件。另外还探讨以上流体力学相关方程的理论与方法在图像处理，数据分析，计算机安全方面的应用。

We will study the properties of global solutions of compressible Navier-Stokes equations with density dependent viscosities and compressible complex fluid equation in 2D or 3D and also effective conditions due to the anisotropic property of thin film. We will also deduce some physical model on viso-elasticity and liquid crystal and then study the blow up mechanism with viscosities and the singularity formation without ones.Furthermore, we will study the dependence of solutions on viscosities and long time behavior of solutions, and more focal point, the well-posedness of isentropic compressible Navier-Stokes equation with density-dependent viscosities. We will also make a try to study the anisotropic.Viscosity in view of various thin film domain and the macro effective boundary conditions, which is contributed to the micro-structure of anisotropic property. In addition, we will also make some practice in image processes, data analysises and computer securities.