Stability of the magnetic Couette-Taylor flow

In this paper we consider the magnetic Couette-Taylor problem, that is, a conducting fluid between two infinite rotating cylinders, subject to a magnetic field parallel to the rotation axis. This configuration admits an equilibrium solution of the form (0, ar br-1,0,0, 0, a + beta log r). It is shown that this equilibrium is Ljapounov stable under small perturbations in {pound}2(Gamma), where Gamma = {(r, cp, z)/r1 < r < r2, p E [0, 2x], z E R}, provided that the parameters a, b, a, /3 are small. The methods of proof are a combination of an energy method, based on Bloch space analysis and small data techniques.