Solvability of a Thermoviscoelastic Model of the Motion of Solutions of Polymers Satisfying the Objectivity Principle

Abstract

The existence of weak solutions of the initial boundary-value problem for a mathematical model describing the motion of weakly concentrated aqueous solutions of polymers is proved. In the model under study, the rheological relation defining the type of the liquid satisfies the objectivity principle. To this end, a smoothed objective Jaumann derivative is considered in the rheological relation. Also, in the mathematical model, the viscosity of the medium depends on temperature, which leads to the appearance of an additional energy balance equation. The proof of the solvability of the problem under consideration is based on the approximation-topological approach to the study of hydrodynamic problems and on the theory of fractional powers of positive operators.