Small Motions of an Ideal Stratified Fluid in a Basin Covered by Ice

Abstract

We study the problem on small motions of the ideal stratified fluid with a free surface partially covered by the crushed ice. The crushed ice is supposed to be ponderable particles of a matter floating on the free surface. These particles do not interact with each other during oscillations of the free boundary (or this interaction is negligible) and stay on the surface during these oscillations. Using the method of orthogonal projection of boundary-value conditions on the free surface and introducing auxiliary problems, we reduce the original initial-boundary problem to the equivalent Cauchy problem for a second-order differential equation in a Hilbert space. We obtain conditions providing the existence of a solution strong with respect to time of the initial-boundary problem describing the evolution of this hydraulic system.