Based on classical Lie Group method, we construct a class of explicit solutions of two-dimensional ideal incompressible magnetohydrodynamics (MHD) equation by its infinitesimal generator. Via these explicit solutions we study the uniqueness and stability of initial-boundary problem on MHD.
Fu-zhi Li. Jia-li Yu. Yang-rong Li. Gan-shan Yang. "Lie Group Solutions of Magnetohydrodynamics Equations and Their Well-Posedness." Abstr. Appl. Anal. 2016 (SI2) 1 - 8, 2016. https://doi.org/10.1155/2016/8183079