Strong solutions of one model of dynamics of thermoviscoelasticity of a continuous medium with memory

A system of equations of dynamics of a thermoviscoelastic continuous medium with an Oldroyd-type rheological relation, which is a generalization of the Navier-Stokes-Fourier system, is considered. In the planar case the existence and uniqueness of strong solutions are established. The proof is based on the construction the Galerkin approximations and their strong estimates which provide the corresponding limit passage.