Vlasov-Poisson-Boltzmann方程研究

本项目研究3维全空间的Vlasov-Poisson-Boltzmann(VPB)方程的若干问题。主要包括VPB方程的谱分析和格林函数的性质，解的最佳衰减速度和逐点性态；由VPB方程严格推导Euler-Poisson方程极限和Navier-Stokes-Poisson方程极限（流体力学极限）；双极VPB方程和修正VPB方程等的谱分析、解的存在唯一性、大时间行为和流体力学极限等。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 concerned with several aspects of the mathematical analysis of Vlasov-Poisson-Boltzmann (VPB) system in the whole space, including the spectral analysis and the property of the Green function of the VPB system, the optimal decay rates and the pointwise behavior of the solution;deriving the fluid dynamical limits (Euler-Poisson system and Navier-Stokes-Poisson system) from the VPB system;the mathematical analysis of the relative models of the VPB system, such as the spectral analysis, existence, uniqueness and long time behavior of the solutions, and fluid dynamical equations for the bipolor VPB system and the modified VPB system.