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We are concerned with the uniform regularity estimates of solutions to thetwo dimensional compressible non-resistive magnetohydrodynamics (MHD) equationswith the no-slip boundary condition on velocity in the half plane. Under theassumption that the initial magnetic field is transverse to the boundary, theuniform conormal energy estimates are established for the solutions tocompressible MHD equations with respect to small viscosity coefficients. As adirect consequence, we proved the inviscid limit of solutions from viscous MHDsystems to the ideal MHD systems in $L^\infty$ sense. It shows that thetransverse magnetic field can prevent the boundary layers from occurring insome physical regime.

Uniform regularity estimates and invisicid limit for the compressible non-resistive magnetohydrodynamics system