Nonstationarity linearizes model of dynamics of nonconpressible viscoelastic fluid

The first initial-boundary value problem for the Oskolkov system of equations modeling in the linear approximation the dynamics of the Kelvin — Voight noncompressible viscoelastic fluid of the zero order is considered. This problem is investigated in the frames of the theory of linear nonhomogenious Sobolev type equations. The existence theorem of the unique solution is proved and the description of the extended phase space of the equation is obtained.