Free boundary problems of magnetohydrodynamics in multi-connected domains

The subject of the paper is the solvability theory of evolution free boundary problems of magnetohydrodynamics for viscous incompressible liquid in multi-connected domains. The main result is the local existence theorem for such problems under rather general assumptions on the initial data of the problem, i.e., on the initial configuration of the liquid and on the initial values of the velocity vector field $v$ and of the magnetic field $H$. The solution is found in anisotropic Sobolev–Slobodetskii spaces.