We consider the regularity of two dimensional incompressible magneto-hydrodynamics equations with zero viscosity. We provide an approximating system to the equations and prove global-in-time existence of classical solution to this approximating system. By using approximating system, a priori estimates for the equations can be justified.
"Regularizing Model for the 2D MHD Equations with Zero Viscosity." Abstr. Appl. Anal. 2012 1 - 7, 2012. https://doi.org/10.1155/2012/212786