Abstract
In this paper, we study the boundary layer problem for the two-dimensional incompressible MHD system with the non-characteristic Dirichlet boundary condition for the velocity and the perfect conducting wall boundary condition for the magnetic field. Using multiscale analysis and the elaborate energy methods, we rigorously prove that the solutions of the viscous and diffusive MHD system are approximated by the inner solutions with the boundary layers in the sense of $L^{2}$ norm when the viscosity and diffusion coefficient tend to zero.
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