Instability of the Forced Magnetohydrodynamics System at Small Reynolds Number

The aim of this paper is to give a result concerning the instability properties of the solutions of forced magnetohydrodynamics equations at small but finite Reynolds numbers. These solutions are highly oscillating spatially on the scale of the underlying flow but are growing on a larger scale depending on the magnetic Reynolds number. The existence of such solutions is called α-effect in the physical litterature. We prove instability results for a dense subset of initial velocity field of the flow at given Reynolds number.