Global free boundary problem for viscous non-homogeneous incompressible magnetohydrodynamics
We consider the motion of viscous non-homogeneous incompresible magnetohydrodynamics in a domain bounded by a free surface. An electromagnetic field generated by some currents in the external domain keeps the magnetohydrodynamic flow in the bounded domain. On the free surface, transmission conditions for electromagnetic fields are imposed. The global-in-time existence of the solution is proved for small initial velocity and vanishing external force. The $L_2$ approach is used. This enables us to treat the transmission conditions.