Abstract: | ![]() In the paper, the solvability of the free boundary problem of magnetohydrodynamics for a viscous incompressible fluid in a simply connected domain is proved. The solution is obtained in the Sobolev–Slobodetskii spaces W22 + l,1 + l/2,1/2 < l < 1 W_2^{2 + l,1 + l/2},1/2 < l < 1 . Bibliography: 15 titles. |