Fast rotation limit for the magnetohydrodynamics equations in a 3D layer

We consider the initial value problem for the incompressible magnetohydrodynamics system with the Coriolis force in a three-dimensional infinite layer. We prove the unique existence of global solutions for initial data in the scaling invariant space when the speed of rotation is sufficiently high. Moreover, we show that the global solution converges to that of the coupled system of the 2D incompressible magnetohydrodynamics equations and the 3D incompressible Maxwell equations as the rotation speed tends to infinity.