Boltzmann型方程的流体动力学极限问题

Boltzmann方程作为统计物理学中的基本方程，与流体力学方程之间存在着重要的联系，其动力学极限问题也一直以来都是许多学者所关注的焦点问题之一。在本项目中，我们拟研究以下两个方面的内容：（1）在周期区域中，Vlasov-Poisson-Boltzmann方程到与之对应的Euler-Poisson流体方程全局极限的问题；（2）在低正则性空间中，Boltzmann方程到相应的流体方程的全局极限问题。

As a basic equation in statistical physics, Boltzmann equation has an important connection with fluid equations, hydrodynamic limits of the Boltzmann equation has always been one of the hottest topics that many scholars are concerned about. In this project, we will focus on the following two topics: (1) Global fluid dynamical limits of the Vlasov-Poisson-Boltzmann to the level of the compressible Euler-Poisson equation in a periodic box; (2) Global hydrodynamic limits of the Boltzmann equation to the level of corresponding fluid equation in low regularity space.