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arXiv · 1111.2288

Instability of the magnetohydrodynamics system at small but finite Reynolds number

Ismaël Bouya
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Abstract

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.

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Ismaël Bouya. 2011-11-09. Instability of the magnetohydrodynamics system at small but finite Reynolds number. https://arxiv.org/abs/1111.2288

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