Possible effect of variation in the internal energy of the free surface of a thin liquid layer on its wavy flow

A formally possible mechanism is considered for the development of longwave perturbations of flow of a thin layer of a heat-conducting viscous liquid with a free boundary, whose characteristic feature is that the Marangoni stresses occurring at the boundary are induced by variations in the internal energy of the interface. The effect of surface internal energy fluctuations on the layer flow in the approximation considered is of a dispersive character, and, in particular, it can facilitate regularization of wave regimes.