This article is cited in 4 papers

To the problem on small motions of the system of two viscoelastic fluids in a fixed vessel

N. D. Kopachevsky

V. I. Vernadsky Crimean Federal University, Simferopol, Russia

Abstract: 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 pencil).

UDC: 517.958

DOI: 10.22363/2413-3639-2018-64-3-547-572