On Weak Solvability for the Navier–Stokes–Voigt Thermal Model with Nonlinear Viscosity Coefficient

The existence of weak solutions to the initial–boundary value problem for the mathematical model describing the motion of a nonlinearly elastically retarded Navier–Stokes–Voigt fluid is studied in this paper. In this model, the fluid viscosity is considered as a nonlinear function. In addition, the temperature is also taken into account, which leads to the emergence of an additional energy balance equation. The proof is based on the topological approximation approach to the study of hydrodynamic problems, as well as the following iterative process.