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This work investigates the incompressible viscous and diffusive MHD system with perfectly conducting wall boundary condition. For different horizontal and vertical viscosities and magnetic diffusions, when they go to zero with different or same speeds, we establish the convergence to the ideal inviscid MHD system and the anisotropic inviscid MHD system by constructing the exact boundary layer functions. (C) 2015 Elsevier Ltd. All rights reserved.
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