MHD方程的非对称和移动标架方法
Asymmetric and Moving-Frame Approaches to MHD Equations
摘要：
具有有限电导率的不可压缩粘性流体的磁流体动力学（MHD）方程描述了粘性导电流体在磁场中的运动。本文用徐的非对称方法和移动标架方法求出了这类方程的十二族解。奇异解族可以反映旋涡的基本特征。其他解是关于空间变量的全局解析解。特别是，伯努利方程和朗斯基行列式在我们的方法中发挥了重要作用。我们的解决方案还可以帮助工程师开发更有效的算法，以找到实际模型的物理数值解。
英文摘要：
The magnetohydrodynamic (MHD) equations of incompressible viscous fluids with finite electrical conductivity describe the motion of viscous electrically conducting fluids in a magnetic field. In this paper, we find twelve families of solutions of these equations by Xu's asymmetric and moving frame methods. A family of singular solutions may reflect basic characteristics of vortices. The other solutions are globally analytic with respect to the spacial variables. In particular, Bernoulli equation and Wronskian determinants play important roles in our approaches. Our solutions may also help engineers to develop more effective algorithms to find physical numeric solutions to practical models.
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