On small motions of hydraulic systems containing a viscoelastic fluid

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.