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This article is cited in 4 scientific papers (total in 4 papers)
MATHEMATICS
Small motions of an ideal stratified fluid partially covered with elastic ice
D. O. Tsvetkov Crimean Federal University, pr. Vernadskogo, 4, Simferopol, Crimea, 295007, Russia
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.
Received: 13.05.2018
Citation:
D. O. Tsvetkov, “Small motions of an ideal stratified fluid partially covered with elastic ice”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 28:3 (2018), 328–347
Linking options:
https://www.mathnet.ru/eng/vuu642 https://www.mathnet.ru/eng/vuu/v28/i3/p328
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Abstract page: | 329 | Full-text PDF : | 154 | References: | 31 |
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