本项目将研究多孔介质中的几类流体力学模型解的性态，包括解的Saint-Venant原则的研究，解的存在唯一性，解对初始数据的连续依赖性以及解对模型本身的结构稳定性等方面，具体来讲有以下几方面：首先将研究解的空间性质，得到解的空间衰减估计；其次研究解的存在唯一性，得到解在齐次临界Besov空间中的存在唯一性；再次研究解对空间几何的连续依赖性，解对初始时间几何的连续依赖性，得到解对初始数据是连续依赖的，由于测量和计算过程中误差时刻存在，所以这部分研究相当重要。接下来我们在有界区域内讨论结构稳定性，主要是想得到在各种不同的边界条件下解对方程本身的连续依赖性以及收敛性,得到一些非零边界条件下的收敛性结果。最后,我们尝试将一些结构稳定性的结果推广到半无限圆柱形区域。

In this project we will study the behaviors of the solutions for some models of fluid mechanics in porous media, which includes the Saint-Venant principle, the existence and uniqueness of the solution, the continuous dependence of solutions on the initial data and the structural stability of the model itself, precisely: Firstly we investigate the spatial behavior of the solution, and obtain the result on the spatial decay estimates of the solution. Secondly we discuss the existence and uniqueness , and obtain the global existence and uniqueness in the homogeneous critical Besov space. Next we discuss the solutions of these models are continuous dependent on the initial spatial geometry and the initial time data. Since the inaccurate may exists in the measuring and computation, thus it's important to study this part. Next we discuss the structural stability of these models in a bounded domain, and we can get some continuous dependence and convergence results under various different boundary conditions. We can obtain some convergence results under nonzero boundary conditions. At last we try to get some structural stability results in an unbounded domain .