Geodesic
Oscillations of stratified liquid partially covered by crumpling ice
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2018), pp. 70-85

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We study the problem on small motions of ideal stratified fluid with a free surface, partially covered by crumbling ice. By the 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 the second order in a Hilbert space. We find sufficient existence conditions for a strong (with respect to the time variable) solution to 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. 
D. O. Tsvetkov. Oscillations of stratified liquid partially covered by crumpling ice. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2018), pp. 70-85. http://geodesic.mathdoc.fr/item/IVM_2018_12_a4/
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     title = {Oscillations of stratified liquid partially covered by crumpling ice},
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[1] Kopachevskii N. D., Temnov A. N., “Kolebaniya stratifitsirovannoi zhidkosti v basseine proizvolnoi formy”, Zh. vychisl. matem. i matem. fiz., 26:5 (1986), 734–755 | MR

[2] Gabov S. A., Sveshnikov A. G., Zadachi dinamiki stratifitsirovannykh zhidkostei, Nauka, M., 1986 | MR

[3] Gabov S. A., Sveshnikov A. G., Lineinye zadachi teorii nestatsionarnykh vnutrennikh voln, Nauka, M., 1990

[4] Gabov S. A., Sveshnikov A. G., “Matematicheskie zadachi dinamiki flotiruyuschei zhidkosti”, Itogi nauki i tekhn.. Ser. Matem. anal., 28, 1990, 3–86 | MR | Zbl

[5] Soldatov M. A., “Kolebaniya zhidkosti v basseine, chastichno pokrytom ldom”, Uchen. zap. SGU, 12:2 (2000), 80–83 | MR

[6] Kopachevskii N. D., Krein S. G., Ngo Zui Kan, Operatornye metody v lineinoi gidrodinamike: Evolyutsionnye i spektralnye zadachi, Nauka, M., 1989

[7] Kopachevskii N. D., Integrodifferentsialnye uravneniya Volterra v gilbertovom prostranstve. Spetsialnyi kurs lektsii, FLP “Bondarenko O. A.”, Simferopol, 2012

[8] Sova M., “Cosine operator functions”, Rozpr. Math., 49 (1966), 1–47 | MR

[9] Ivanov V. K., Melnikova I. V., Filinkov A. I., Differentsialno-operatornye uravneniya i nekorrektnye zadachi, Fizmatlit, M., 1995