Abstract
We present the \(L_p\)-theory of solvability of free boundary problems of magnetohydrodynamics of viscous incompressible fluids in multi-connected domains constructed in the paper Solonnikov (Interf Free Bound 14:569–603, 2012) for \(p=2\). The case of simply connected domains is studied in Padula and Solonnikov (J Math Sci 178:313–344, 2011), Solonnikov (\(L_p\)-theory of free boundary problems of magnetohydrodynamics in simply connected domains, submitted to AMS Translations).
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