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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2024. Vol 48

On an Initial-boundary Value Problem Which Arises in the Dynamics of a Compressible Ideal Stratified Fluid

Author(s)
Denis O. Tsvetkov1

1Crimean Federal University, Simferopol, Russian Federation

Abstract
In this paper, we investigate the problem on small motions of a compressible ideal stratified fluid in a bounded domain. The problem is studied on the base of approach connected with application of so-called operator matrices theory, as well as abstract differential operator equations. For this purpose, Hilbert spaces and some of their subspaces are introduced. The original initial-boundary value problem reduces to the Cauchy problem for a second-order differential operator equation in the orthogonal sum of some Hilbert spaces. Further, an equation with a closed operator is associated with the resulting equation. On this basis, sufficient conditions for the existence of a solution to the corresponding problem are found.
About the Authors
Denis O. Tsvetkov, Cand. Sci. (Phys.Math.), Assoc. Prof., Crimean Federal University, Institute of Physics and Technology, Simferopol, 295000, Russian Federation, tsvetdo@gmail.com
For citation

Tsvetkov D. O. On an Initial-boundary Value Problem Which Arises in the Dynamics of a Compressible Ideal Stratified Fluid. The Bulletin of Irkutsk State University. Series Mathematics, 2024, vol. 48, pp. 49–63. (in Russian)

https://doi.org/10.26516/1997-7670.2024.48.49

Keywords
compressible stratified fluid, initial boundary value problem
UDC
517.98
MSC
35D35 35Q99
DOI
https://doi.org/10.26516/1997-7670.2024.48.49
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