带外力场的Boltzmann方程研究

本项目主要对带外力场的Boltzmann方程进行数学理论分析研究。Boltzmann方程是描述稀薄气体运动过程的基本方程之一，当气体中的带电粒子受到电场作用时，其运动过程由Vlasov-Poisson-Boltzmann（VPB）方程描述；当气体中的带电粒子受到电场和磁场作用时，其运动过程由Vlasov-Maxwell-Boltzmann（VMB）方程描述。本项目主要研究VPB方程和VMB方程的谱分析、格林函数、解的最优衰减速度和逐点性态、流体动力学极限（由VPB（VMB）方程推导Euler-Poisson（Maxwell）方程极限和Navier-Stokes-Poisson（Maxwell）方程极限）等问题。项目所研究的内容具有很强的应用科学背景，是国际上十分重视、具有前沿性的研究课题之一。

In this project, we are concern with the mathematical analysis of the Boltzmann equations with external forces. The Boltzmann equation is the fundamental model describing the motion of the particles of the diluted gases. When the particles are under the influence of the electric fields, the motions of the particles are described by the Vlasov-Poisson-Boltzmann (VPB) system; when the particles are under the influence of the electric and magnetic fields, the motions of the particles are described Vlasov-Maxwell-Boltzmann system. In this project, we are mainly consider the spectral analysis, Green's function, the optimal decay rates and the pointwise estimates of the solution； the fluid dynamical limits (Euler-Poisson(Maxwell) system limits and Navier-Stokes-Poisson(Maxwell) system limits) of the VPB(VMB) system.