Vanishing Shear Viscosity Limit in the Magnetohydrodynamic Equations |
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| Authors: | Jishan Fan Song Jiang Gen Nakamura |
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| Affiliation: | (1) College of Information Sciences and Technology, Nanjing Forestry University, Nanjing, 210037, P.R. China;(2) Department of Mathematics, Suzhou University, Suzhou, 215006, P.R. China;(3) Institute of Applied Physics and Computational Mathematics, P. O. Box 8009, Beijing, 100088, P.R. China;(4) Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan |
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| Abstract: | We study an initial boundary value problem for the equations of plane magnetohydrodynamic compressible flows, and prove that as the shear viscosity goes to zero, global weak solutions converge to a solution of the original equations with zero shear viscosity. As a by-product, this paper improves the related results obtained by Frid and Shelukhin for the case when the magnetic effect is neglected. Supported by NSFC (Grant No. 10301014, 10225105) and the National Basic Research Program (Grant No. 2005CB321700) of China. |
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