本项目拟研究磁流体方程的能控性，主要内容包括：(1)无磁扩散的不可压缩磁流体方程的能控性；(2)可压缩磁流体方程施加局部控制的能控性；(3)非等熵可压缩磁流体方程的能控性；(4)具霍尔效应的可压缩磁流体方程的能控性。磁流体方程是由Navier-Stokes方程和Maxwell方程耦合的方程组，用来描述导电流体与电磁场之间的相互作用，是一类重要的流体力学方程。对其能控性的研究涉及双曲抛物结构，多重非线性、退化性和奇异性等典型的数学困难。本项目希望通过研究磁流体方程的能控性，揭示出磁场控制在改变流体动力学行为方面的作用和能力，探索出解决流体力学方程能控性问题的新思路和新方法。

This project is devoted to studying the controllability of the magnetohydrodynamics equations. The main contents include: (1) the controllability of the incompressible magnetohydrodynamics equations without magnetic diffusion; (2) the controllability of the compressible magnetohydrodynamics equations with local control functions; (3) the controllability of the non-isentropic compressible magnetohydrodynamics equations; (4) the controllability of the compressible Hall-magnetohydrodynamics equations. The magnetohydrodynamics equations are a combination of the Navier-Stokes equations and the Maxwell's equations. They are a kind of important fluid mechanics equations which are used to describe the interaction between electromagnetic field and conductive fluid. The study on this system is related to typical difficulties in mathematics such as the coupling of hyperbolic-parabolic system, nonlinearity, degradation and singularity. By studying the controllability of magnetohydrodynamics equations, we hope to discover the role and ability of magnetic field control in changing the dynamic behavior of the fluid and develop some new methods and ways of thinking for the controllability of fluid mechanics equations.