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Abstract and Applied Analysis
Volume 2016, Article ID 8183079, 8 pages
Research Article

Lie Group Solutions of Magnetohydrodynamics Equations and Their Well-Posedness

1School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
2School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China
3School of Mathematics and Computer Science, Yunnan Minzu University, Kunming, Yunnan 650500, China

Received 27 June 2016; Accepted 20 September 2016

Academic Editor: Bingwen Liu

Copyright © 2016 Fu-zhi Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.