两相流MHD模型的一些问题研究

本项目主要研究在磁场作用下的可压缩等熵两相流模型，简称为可压缩两相流MHD方程组。该模型是描述在磁场作用下的两相(two-phase)混合物运动的基本模型之一，在科学和工程上具有广泛的应用。这个模型是由申请人和合作者对Vlasov-Fokker-Planck/MHD方程组取伸缩参数ε→0的极限而得到的。由于对于从可压缩Vlasov-Fokker-Planck/MHD方程组收敛到两相流MHD模型还没有严格的数学证明，本项目将围绕该问题以及两相流MHD模型参数消失极限等问题开展系统的研究，以期取得一些新的进展。

This project is concerned with a compressible isentropic two-phase model with magnetic field which is called compressible two-phase MHD model. This model is often used to describe the motion of a two-phase mixture under the impact of magnetic field, which has a wide range of applications in science and engineering.This model is formally derived by taking scaling limits ε→0 from the Vlasov-Fokker-Planck/compressible MHD system. However, a rigorous proof for the process as ε→0 is still open. Therefore in this project we will consider this problem and some other vanishing parameters limits of the system, We expect a breakthrough in these aspects.