有界区域上Vlasov–Poisson/Maxwell–Boltzmann方程组的数学理论

Vlasov-Poisson-Boltzmann(VPB)方程组和Vlasov-Maxwell-Boltzmann(VMB)方程组是等离子体物理中的基本模型。 .本项目研究有界区域上VPB方程组和VMB方程组的数学理论，主要包括：软势情形的单极VPB方程组在初值靠近平衡态时解的适定性；硬势情形的双极VPB方程组在初值靠近平衡态时解的适定性；VPB方程组到可压Euler-Poisson方程组、不可压Euler方程组和不可压Navier-Stokes方程组的收敛性；单极VMB方程组在初值靠近平衡态时解的适定以及它到不可压Navier-Stokes-Maxwell方程组和不可压磁流体力学方程组的收敛性等等。.上述研究内容不仅是国际数学界和应用数学界十分重视的、前沿的、具有主流兴趣的重要研究课题，有极其重要的理论意义，而且紧密联系应用科学和工程技术实际，有十分广泛的应用前景。

Vlasov-Poisson-Boltzmann (VPB) system and Vlasov-Maxwell-Boltzmann (VMB) system are fundamental models in plasma physics. .This project investigates the mathematical theory of the VPB system and VMB system in bounded domains, mainly including: the well-posedness of the unipolar VPB system with soft potential when the initial data are close to the equilibrium state; the well-posedness of bipolar VPB system with hard potential when the initial data are close to the equilibrium state; convergence of the solutions of the unipolar VPB system to that of the compressible Euler-Poisson equations, the incompressible Euler equations or the incompressible Navier-Stokes equations; the well-posedness of unipolar VMB system with hard sphere when the initial data is close to the equilibrium state and the convergence of solution of it to that of the incompressible Navier-Stokes-Maxwell system or the incompressible magnetohydrodynamic system.. The above-mentioned research topics are not only very important in international mathematics and applied mathematics community which attach the forefront of mainstream interest, but also extremely important in theoretical significance. There are very broad application prospects in science and engineering.