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Russia Simferopol
Section  Mathematics 
Title  Small motions of an ideal stratified fluid partially covered with elastic ice 
Author(s)  Tsvetkov D.O.^{a} 
Affiliations  Crimea Federal University^{a} 
Abstract  We study the problem of small motions of an ideal stratified fluid with a free surface, partially covered with elastic ice. Elastic ice is modeled by an elastic plate. The problem is studied on the basis of an approach connected with application of the socalled operator matrices theory. To this end we introduce Hilbert spaces and some of their subspaces as well as auxiliary boundary value problems. The initial boundary value problem is reduced to the Cauchy problem for the differential secondorder equation in Hilbert space. After a detailed study of the properties of the operator coefficients corresponding to the resulting system of equations, we prove a theorem on the strong solvability of the Cauchy problem obtained on a finite time interval. On this basis, we find sufficient conditions for the existence of a strong (with respect to the time variable) solution of the initialboundary value problem describing the evolution of the hydrosystem. 
Keywords  stratification effect in ideal fluids, initial boundary value problem, differential equation in Hilbert space, Cauchy problem, strong solution 
UDC  517.98 
MSC  35D35, 47D03 
DOI  10.20537/vm180305 
Received  13 May 2018 
Language  Russian 
Citation  Tsvetkov D.O. Small motions of an ideal stratified fluid partially covered with elastic ice, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2018, vol. 28, issue 3, pp. 328347. 
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