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Home » Issues » Archive of Issues » 2023 - 4 issue » pp. 625–641

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Russia Simferopol
Year
2023
Volume
33
Issue
4
Pages
625–641
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Section Mathematics
Title Initial-boundary value problem for the equations of dynamics of a rotating viscous stratified fluid
Author(-s) Tsvetkov D.O.a
Affiliations Crimea Federal Universitya
Abstract We study the problem of small motions of a viscous stratified fluid partially filling a container that uniformly rotates around an axis co-directed by gravity. The problem is studied on the basis of an approach related to the application of the so-called operator matrix theory. To this end, we introduce Hilbert spaces and some their subspaces, as well as auxiliary boundary value problems. The original initial-boundary value problem is reduced to the Cauchy problem for a first-order differential equation in some 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 solvability of the Cauchy problem. On this basis, we find sufficient conditions for the existence of a solution of the original initial-boundary value problem describing the evolution of the hydro-system.
Keywords stratification effect in viscous fluids, differential equation in Hilbert space, Cauchy problem
UDC 517.98
MSC 76D50, 34G10, 47B25, 76U05
DOI 10.35634/vm230406
Received 25 September 2023
Language Russian
Citation Tsvetkov D.O. Initial-boundary value problem for the equations of dynamics of a rotating viscous stratified fluid, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2023, vol. 33, issue 4, pp. 625–641.
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