Crumbled ice on the surface of a multilayered fluid

We study the problem of the small motions and normal oscillations of a system of two ideal fluids with a free surface partially covered with crumbled ice. By crumbled ice we mean the situation in which heavy particles of some substance float on the free surface and these particles do not interact (or the interaction is small enough to be neglected) when the free surface oscillates. We find sufficient conditions for the existence of a strong solution (with respect to the time variable) to the initial boundary value problem describing the evolution of the specified system. We also study the spectrum of normal oscillations, basic properties of the eigenfunctions, and other questions.