Navier-Stokes/MHD方程来源于流体力学中重要的偏微分方程，不仅具有很强的非线性，而且常带有退化性，强耦合性，它们一直是应用数学和计算流体力学研究的前沿问题，本项目拟从数学理论研究的角度出发研究流体力学中的若干问题，其中主要包括：.（1）.当热传导系数为常数且初始密度含真空（即初始密度大于或等于0）时，一维（或柱对称，球对称）可压缩非等熵Navier-Stokes初边值问题的全局强解的存在性及长时间性质。.（2）.当热传导系数为常数且初始密度含真空时，一维（或柱对称）可压缩非等熵MHD初边值问题的全局强解的存在性和长时间性质。.（3）.一维（或柱对称）可压缩非等熵MHD初边值问题的零磁扩散极限过程、磁边界层效应。

Navier-Stokes equations and MHD equations are important differential equations in fluid dynamics. They are not only nonlinear But also degenerate and strong coupling. These PDEshave been central issue in both applied mathematics and computational mechanics. In this project, we aim to study some mathematically important problem from fluid mechanics. It mainly consists of the following parts:.（1）When the heat conductivity coefficient is constant and the initial density contains vacuum, global existence and large time behavior of the strong(or classical)solutions for the one dimensional (or spherically symmetric、 cylindrical symmetric) non-isentropic compressible Navier-Stokes initial-boundary value problem..（2）When the heat conductivity is constant and the initial density contains vacuum, global existence and large time behavior of the strong(or classical) solutions for the one dimensional (or cylindrically symmetric) non-isentropic compressible MHD initial-boundary value problem..（3）vanishing resistivity limit and the effects of the magnetic boundary layer for the one-dimensional（or cylindrically symmetric） non-isentropic compressible MHD initial-boundary value problem.