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In this paper we consider the long time well-posedness of solutions to twodimensional compressible magnetohydrodynamics (MHD) boundary layer equations.When the initial data is a small perturbation of a steady solution with size of$\varepsilon$ and the far-field state is also a small perturbation around sucha steady solution in Sobolev space, then the lifespan of solutions is proved tobe greater than $\varepsilon^{-\frac43}$.

Long time well-posedness of compressible magnetohydrodynamics boundary layer equations in Sobolev space