In this paper we consider the compressible models of magnetohydrodynamic flows giving rise to a variety of mathematical problems in many areas. We study the asymptotic limit for the compressible rotational magnetohydrodynamic flows with the well-prepared initial data such that we derive a rigorous quasi-geostrophic equation with diffusion term governed by the magnetic field from a compressible rotational magnetohydrodynamic flows. This paper covers two results: the existence of the unique global strong solution of quasi-geostrophic equation with good regularity on the velocity and magnetic field and the derivation of quasi-geostrophic equation with diffusion.
- Asymptotic limit
- Magnetohydrodynamic flows