On Small Motions of Hydrodynamic Systems Containing a Viscoelastic Fluid
E. V. Plokhaya · Lobachevskii Journal of Mathematics · 2021
Abstract This paper is devoted to small motions problem of composite hydrodynamic systems containing a viscoelastic fluid. Hydrodynamic systems of two or more viscoelastic fluids are considered, as well as partially dissipative systems containing ideal fluids or a barotropic gas (in addition to a viscoelastic fluid). The listed initial-boundary-value problems are investigated using the operator approach developed by N. D. Kopachevsky. This approach makes it possible to pass from the initial-boundary-value problem to the Cauchy problem for an operator-differential equation in the sum of Hilbert spaces and to prove the correct solvability theorem.