Малые движения идеальной стратифицированной жидкости со свободной поверхностью, полностью покрытой упругим льдом

We study the problem on small oscillations of an ideal stratified fluid in a vessel with a free surface completely covered with the elastic ice. The developed approach is based on application of the theory of operator matrices acting in the Hilbert space, the initial boundary value problem is reduced to the Cauchy problem for differential-operator of a special form. For this Cauchy problem a theorem on strong solvability is proved.