Geodesic
On small motions of hydraulic systems containing a viscoelastic fluid
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 3, Tome 172 (2019), pp. 48-90

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This paper is devoted to the study of two problems describing small motions of partially dissipative hydraulic systems. The first problem concerns small motions of a hydraulic system consisting of a viscoelastic fluid and a barotropic gas located above the fluid; the second concerns small motions of the hydraulic system “viscoelastic fluid—ideal fluid—ideal fluid” filling a static vessel. Using the operator approach developed in previous works of the authors, both problems are reduced to the Cauchy problem for a differential-operator equation in a Hilbert space and a theorem on the solvability of the problem on an arbitrary finite time interval is proved.
Keywords: hydrodynamic system, ideal fluid, viscoelastic fluid, orthoprojector, Cauchy problem.
Mots-clés : barotropic gas 
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N. D. Kopachevskii; E. V. Syomkina. On small motions of hydraulic systems containing a viscoelastic fluid. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 3, Tome 172 (2019), pp. 48-90. http://geodesic.mathdoc.fr/item/INTO_2019_172_a4/