Cucker-Smale模型是研究自然界中群体行为的一个简化模型，当群体的数目充分大时，借鉴统计物理学思想推导出的kinetic Cucker-Smale模型是连接微观模型与宏观模型之间的桥梁. 如果考虑布朗效应，我们还可以在kinetic Cucker-Smale模型中引入扩散项得到一个Fokker-Planck型方程，此类方程允许有稳态解存在，我们将在稳态解附近分析光滑解的适定性，并研究光滑解收敛到稳态解的速度. 如果考虑群体周围介质的影响，我们还可以得到kinetic Cucker-Smale模型同流体力学方程相耦合的模型. 在本项目中我们还将研究kinetic Cucker-Smale模型同不可压缩Navier-Stokes方程相耦合模型强解的适定性,并分析强解的大时间行为.

Cucker-Smale model is a simplified model for studying collective behaviors in nature. When the number of a group is sufficiently large, using the idea in statistical physics, we can derive the kinetic Cucker-Smale model, which is a bridge connecting the microscopic model to the macroscopic one. If the Brownian effect is taken into account, we can introduce the diffusion term into the kinetic Cucker-Smale model to obtain a kinetic equation of the Fokker-Planck type. This tye of model admits existence of the steady solution. We will analyze the well-posedness of smooth solutions under small smooth perturbations and study the convergence rate of smooth solutions to the steady solution. Considering the influence of the surrounding medium, we can also get the kinetic Cucker-Smale model coupled with fluid equations. In this project, we will also study the well-posedness and large time behaviors of strong solutions to the kinetic Cucker-Smale model coupled with incompressible Navier-Stokes equations.