Abstract 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.
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