Singular Limit of the Rotational Compressible Magnetohydrodynamic Flows

We consider the compressible models of magnetohydrodynamic flows giving rise to a variety of mathematical problems in many areas. We derive a rigorous quasi-geostrophic equation governed by magnetic field from the stratified flows of the rotational compressible magnetohydrodynamic flows with the well-prepared initial data and the tool of proof is based on the relative entropy. Furthermore, the convergence rates are obtained.

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