The Generalized Linearized Model of Incompressible Viscoelastic Fluid of Nonzero Order

In the frames of the non-autonomous sobolev type equations The Cauchy–Dirichlet problem for the generalized linearized Oskolkov's system modeling thermoconvection of the incompressible viscoelastic fluid of the nonzero order is considered. The theorem of the existence of the unique solution of this problem is proved and the description of its extended phase space is received.