The thermoconvection problem for the linearizied model of the incompressible viscoelastic fluid of the nonzero order

The Cauchy–Dirichlet problem for the linearized system modeling thermoconvection of the incompressible viscoelastic fluid of the nonzero order is considered. This problem is investigated on the base of the theory of relatively $p$-sectorial operators and degenerative semi-groups of operators. The theorem of the existence of the unique solution of this problem is proved and the description of its extended phase space is received.