Solvability of one class of thermo-visco-elastic-models

The existence of a weak solution to the initial-boundary value problems for the mathematical models of an incompressible non-Newtonian fluids (namely, for the linear elastically retarded fluid and for a weak concentrated aqueous polymer solutions with total and objective derivatives at the rheological relation) in 2D and 3D bounded domains is studied in this paper. In this mathematical models the viscosity depends on a temperature, which leads to emergence of the additional heat balance equation (it is a parabolic equation with non-smooth coefficients and with right part from L1(0, T; L1(Ω))). © 2018 Author(s).