  We study an anisotropic system arising in magnetohydrodynamics (MHD) in the
whole space R^3 , in the case where there are no diffusivity in the vertical
direction and only a small diffusivity in the horizontal direction (of size
$\epsilon$$\alpha$ with 0 \textless{} $\alpha$ $\le$ $\alpha$0, for some
$\alpha$0 \textgreater{} 0). We prove the local existence and uniqueness of a
strong solution and then, using Strichartz-type estimates, we prove that this
solution globally exists in time for large initial data, when the rotation is
fast enough.
