Stability of the magnetic Couette-Taylor flow
Scarpellini, B.
In: Zeitschrift für angewandte Mathematik und Physik ZAMP, 2005, vol. 56, no. 3, p. 412-438
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- 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). $ It is shown that this equilibrium is Ljapounov stable under small perturbations in $ \mathcal{L}^{2} (\Gamma ), $ where $ \Gamma = \{ (r,\varphi ,z)/r_{1} < r < r_{2} ,\varphi \in [0,2\pi ],z \in \mathbb{R}\} , $ provided that the parameters a, b, α, β are small. The methods of proof are a combination of an energy method, based on Bloch space analysis and small data techniques