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Pré-Publication, Document De Travail Année : 2011

Instability of the magnetohydrodynamic system at small but finite Reynolds number

Résumé

The aim of this paper is to give a result concerning the stability properties of the solutions of magnetohydrodynamics equations at small but finite Reynolds numbers. These solutions are found using the alpha-effect: this method gives us solutions which are highly oscillating spatially on the scale of the underlying flow but are growing on a larger scale depending on a parameter epsilon. We prove nonlinear stability and instability results for a dense subset of initial velocity field of the flow at given Reynolds number.

Dates et versions

hal-00642821 , version 1 (18-11-2011)

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Ismaël Bouya. Instability of the magnetohydrodynamic system at small but finite Reynolds number. 2011. ⟨hal-00642821⟩
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