We study the problem of small motions of an ideal stratified liquid with a free surface totally covered by an elastic ice. The elastic ice is modeled by an elastic plate. We reduce the original initial boundary value problem to an equivalent Cauchy problem for a second-order differential equation in a Hilbert space. We obtain conditions under which there exists a strong (with respect to time) solution of the initial boundary value problem describing the evolution of the hydrodynamic system under consideration. We also study the spectrum of normal oscillations, the basic properties of the eigenfunctions.
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