To the Problem on Small Motions of the System of Two Viscoelastic Fluids in a Fixed Vessel
Journal: Contemporary Mathematics Fundamental Directions
Year: 2018

In this paper, we study the problem of small motions of two Oldroyd viscoelastic incompressible ﬂuids contained in a ﬁxed vessel. By means of the operator approach, we reduce the original initialboundary value problem to the Cauchy problem for a diﬀerential operator equation in a Hilbert space and prove the well-posed solvability of the problem on an arbitrary interval of time. We obtain the equation for normal oscillations of the hydraulic system under consideration (Krein generalized operator