可压缩Navier-Stokes-Maxwell方程组的数学理论

本项目主要研究可压缩Navier-Stokes-Maxwell方程组的数学理论。 主要包括可压缩Navier-Stokes-Maxwell方程组弱解的存在性理论、可压缩Navier-Stokes- Maxwell方程组在初值靠近平衡态附近时古典解的整体存在性和渐近行为、可压缩Navier- Stokes-Maxwell方程组的零Mach数极限、 可压缩Navier-Stokes-Maxwell方程组到磁流体力学方程组的收敛性、可压缩Navier-Stokes-Maxwell方程组到可压缩Euler-Maxwell方程组和可压缩Navier-Stokes-Poisson方程组的收敛性问题等等。.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。

This project mainly aims to deal with the mathematical theory of compressible Navier-Stokes-Maxwell system. These include the existence theory of weak solution to the compressible Navier-Stokes-Maxwell system, the global existence and asymptotic behavior of classical solutions to the compressible Navier-Stokes- Maxwell system near the equilibrium, the low Mach number limit of compressible Navier-Stokes-Maxwell system, the convergence of compressible Navier-Stokes -Maxwell system to the compressible magnetohydrodynamic equations, the convergence of compressible Navier-Stokes-Maxwell system to the compressible Euler-Maxwell equations, the convergence of the compressible Navier-Stokes-Maxwell system to compressible Navier-Stokes-Poisson system, and so on.. .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.