Phase space of the initial-boundary value problem for the Oskolkov system of nonzero order

The phase space of the Dirichlet initial-boundary value problem for a system of partial differential equations modeling the flow of an incompressible viscoelastic Kelvin-Voigt fluid of nonzero order is described. The investigation is based on the theory of semilinear Sobolev-type equations and the concepts of a relatively spectral bounded operator and a quasi-stationary trajectory for the corresponding Oskolkov system modeling the plane-parallel flow of the above fluid.