Geodesic
Small movements of a system of ideal stratified fluids completely covered with crumbled ice
The Bulletin of Irkutsk State University. Series Mathematics, Tome 26 (2018), pp. 105-120

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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. 
@article{IIGUM_2018_26_a7,
     author = {D. O. Tsvetkov},
     title = {Small movements of a system of ideal stratified fluids completely covered with crumbled ice},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {105--120},
     publisher = {mathdoc},
     volume = {26},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2018_26_a7/}
}
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D. O. Tsvetkov. Small movements of a system of ideal stratified fluids completely covered with crumbled ice. The Bulletin of Irkutsk State University. Series Mathematics, Tome 26 (2018), pp. 105-120. http://geodesic.mathdoc.fr/item/IIGUM_2018_26_a7/