Global existence of large solutions to the planar magnetohydrodynamic equations with zero magnetic diffusivity

Abstract In this paper, we consider the initial-boundary value problem to the planar magnetohydrodynamic (MHD) equations with zero magnetic diffusivity. In the case when the coefficients of viscosity and heat conductivity are positive constants, we establish the global existence and uniqueness of strong solution by the a priori estimates. The results are obtained without any smallness restriction to the initial data and the initial density allows vacuum.

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