Small Movements of a System of Ideal Stratified Fluids Completely Covered with Crumbled Ice

Abstract

We study the problem on small motions of two non mixing ideal stratified fluids with a free surface, covered with crumbling ice. Using method of orthogonal projecting the boundary conditions on the moving surface and the introduction of auxiliary problems of the original initial-boundary value problem is reduced to the equivalent Cauchy problem for a differential equation of second order in some Hilbert space. We find sufficient existence conditions for a strong (with respect to the time variable) solution of the initial-boundary value problem describing the evolution of the specified hydrodynamics system.

Keywords

• stratification effect in ideal fluids
• initial boundary value problem
• differential equation in Hilbert space
• Cauchy problem
• strong solution