On the initial-boundary problem for thermocapillary motion of an emulsion in space

The paper is devoted to the study of the initial-boundary problem for thermocapillary motion of an emulsion in closed bounded domain with sufficiently smooth boundary in the absence of gravity. With the use of Tikhonov–Shauder fixed point theorem the local in time solvability to the problem with zero mean volume velocity of the mixture and zero heat flux on the boundary is proved.