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Home » Issues » Archive of Issues » 2018 - 3 issue » pp. 328-347

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Russia Simferopol
Year
2018
Volume
28
Issue
3
Pages
328-347
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Section Mathematics
Title Small motions of an ideal stratified fluid partially covered with elastic ice
Author(-s) Tsvetkov D.O.a
Affiliations Crimea Federal Universitya
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 so-called 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 second-order 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 initial-boundary 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. 328-347.
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