Asymmetric and moving-frame approaches to MHD equations

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 eight 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. Our solutions may help engineers to develop more effective algorithms to find physical numeric solutions to practical models.