Geodesic
Crumbled ice on~the~surface of~a~multilayered fluid
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 777-801

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We study the problem of the small motions and normal oscillations of a system of two ideal fluids with a free surface partially covered with crumbled ice. By crumbled ice we mean the situation in which heavy particles of some substance float on the free surface and these particles do not interact (or the interaction is small enough to be neglected) when the free surface oscillates. We find sufficient conditions for the existence of a strong solution (with respect to the time variable) to the initial boundary value problem describing the evolution of the specified system. We also study the spectrum of normal oscillations, basic properties of the eigenfunctions, and other questions.
Keywords: initial boundary value problem, differential equation in Hilbert space, Cauchy problem, strong solution, spectral problem. 
@article{SEMR_2020_17_a93,
     author = {D. O. Tsvetkov},
     title = {Crumbled ice on~the~surface of~a~multilayered fluid},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {777--801},
     publisher = {mathdoc},
     volume = {17},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a93/}
}
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D. O. Tsvetkov. Crumbled ice on~the~surface of~a~multilayered fluid. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 777-801. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a93/