Boltzmann方程是输运理论中描述稀薄气体运动分布的基本方程，它与现代物理学、力学及工程中的许多课题都有密切的联系。本项目主要研究没有角截断或者有角截断的Boltzmann方程和Landau方程等相关动理学方程的数学理论，包括靠近平衡态或者不靠近平衡态时动理学方程全局解的适定性、动理学方程的谱分析及解的正则性、流体力学极限等问题。这些问题均为国际上前沿的、极受重视的数学问题，具有重要的理论意义和广泛的应用价值。

Boltzmann equation is a fundamental partial differential equation in the Transport Theory, which is used to describe the dynamics of the rarefied gas. It has a very close relation to modern physics、mechanics and plenty of subjects in engineering. This project mainly studies mathematical problems of kinetic equations, including the Boltzmann equation with or without angular cutoff, Landau equation and so on. These problems include global well-posedness of global solutions、spectrum analysis of the kinetic equations、regularity theory of the.solution、mutual relation of kinetic equations and hydrodynamical equations and the related mathematical problems. The above mentioned study contents are important in the international mathematical field, of the cutting edge, and of important theoretical study interests and comprehensive applicable value.