On Small Motions of Hydraulic Systems Containing Viscoelastic Fluid

• Published in: Journal of mathematical sciences (New York, N.Y.) Vol. 267; no. 6; pp. 716 - 759
• Main Authors: Kopachevsky, N. D., Syomkina, E. V.
• Format: Journal Article
• Language: English
• Published: New York Springer US 04.11.2022; Springer; Springer Nature B.V
• Subjects: Cauchy problems; Differential equations; Hilbert space; Hydraulic equipment; Ideal fluids; Industrial equipment; Mathematics; Mathematics and Statistics; Operators (mathematics); Viscoelastic fluids; barotropic gas; viscoelastic fluid; 39B42; ideal fluid; 39A14; orthoprojector; hydrodynamic system; 76D05; 35Q30; Cauchy problem
• ISSN: 1072-3374; 1573-8795; 1573-8795
• DOI: 10.1007/s10958-022-06165-4

In this paper, we study 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” in an immovable vessel. Using the operator approach developed in previous works of the authors, we reduce both problems to the Cauchy problem for a differential-operator equation in a Hilbert space and prove a theorem on the solvability of the problem on an arbitrary finite time interval.