This paper presents the local well-posedness of the strong solutions to the 2D incompressible magnetohydrodynamics(MHD) equations without magnetic diffusion in a strip domain. Via a semi-discrete Galerkin scheme, we construct approximate solutions with Navier-type boundary conditions, and can have solutions by passing the limit. Moreover, our results are valid for the Cauchy problem.
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Songshang Yang (2024) studied this question.
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