Existence of weak solutions to the time-dependent MHD equations coupled to the heat equation with nonlocal radiation boundary conditions (Q1021943)

The coupling of the system of magnetohydrodynamics to the heat equation in context of an application to crystal growth is studied. The heat sources are given by the dissipation of current that occurs in the fixed conductors of the system. Following the Boussinesq model the dissipative heating is neglected in the fluid. For the magnetic field the natural interface conditions are taken into account, while the nonlocal radiation boundary conditions are used for the heat flux. The existence of a weak solution with a defect measure is proven -- concentrated in a singular set.