Об устойчивости совместного движения двух слоев идеальных жидкостей

The small perturbations evolution of two layers joint motion of ideal incompressible fluids on a solid substrate is studied. It is shown that the linearized problem in Lagrangian coordinates allows for the separation of variables. A system of amplitude equations is obtained, which contains two Weber numbers, the ratio of densities and initial layer thicknesses, as well as dimensionless wave numbers. The presented results of the asymptotic and numerical analysis of the amplitude equations indicate the stability of the layers motion