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Received 22.06.2020, received in revised form 02.07.2020, accepted 20.09.2020 Abstract. In the work the 3D two-layer motion of liquids, the velocity field of which has a special form, is considered. The arising conjugate initial boundary value problem for the Oberbek–Boussinesq model is reduced to a system of ten integrodifferential equations with full conditions on a flat interface. It is shown that for small Marangoni numbers the stationary problem can have up to two solutions. The case when the stationary flow arises due to a change in the internal interphase energy is analyzed separately.

On a Creeping 3D Convective Motion of Fluids with an Isothermal Interface