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

The Cauchy–Dirichlet problem for the hybrid of linearizied Oskolkov system and heat equation in the approximation of Oberbek–Bussinesq modeling thermoconvection of incompressible viscoelastic fluid is considered. This problem is investigated on the base of the theory of relatively $p$-sectorial operators and degenerate semigroups of operators. The theorem of existence of the unique solution of this problem is proved and the description of its extended phase space is received.