On weak solvability of the Navier-Stokes-Voigt thermal model with nonlinear viscosity coefficient

The existence of weak solutions to the initial–boundary value problem for a 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 being considered as a nonlinear function. Also in this model the temperature is taken into account, which leading to the emergence of an additional energy balance equation. The proof is based on the topological approximation approach to the study hydrodynamic problems, as well as the following iterative process.