Abstract
The chapter concerns the unsteady motion of two fluids separated by a closed unknown interface Γt in the Oberbeck-Boussinesq approximation (see, for example, [49]). It means that the right-hand side of the problem depends on the temperature in a specific way. On the interface between the liquids, the surface tension is taken into account. This problem is investigated in the Holder classes of functions, where local existence theorem for the problem is proved at first. As the solvability of the temperature-independent problem has been already obtained and the diffraction problem for the heat equation is studied by well-known methods, the existence of a solution to the complete problem is proved by successive approximations.
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