Abstract
We consider the following problem in the MHD approximation: the vessel Ω 1 ⊂ Ω is filled with an incompressible, electrically conducting fluid, and is surrounded by a dielectric or by vacuum, occupying the bounded domain Ω 2 = Ω ∖ Ω 1 . In Ω we have a magnetic and electric field and the external surface S = ∂ Ω is an ideal conductor. The emphasis in the paper is on when Ω is not simply connected, in which case the MHD system is degenerate. We use Hodge-type decomposition theorems to obtain strong solutions locally in time or global for small enough initial data, and a linearization principle for the stability of a stationary solution.
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