| Abstract: | 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,\alpha + \beta \log r).
$
(0,ar + br^{{ - 1}} ,0,0,0,\alpha + \beta \log r).
It is shown that this equilibrium is Ljapounov stable under small perturbations in
$
\mathcal{L}^{2} (\Gamma ),
$
\mathcal{L}^{2} (\Gamma ),
where
$
\Gamma = \{ (r,\varphi ,z)/r_{1} < r < r_{2} ,\varphi \in 0,2\pi ],z \in \mathbb{R}\} ,
$
\Gamma = \{ (r,\varphi ,z)/r_{1} < r < r_{2} ,\varphi \in 0,2\pi ],z \in \mathbb{R}\} ,
provided that the parameters a, b,  ,  are small. The methods of proof are a combination of an energy method, based on Bloch space analysis and small data techniques. |
