On the Boundary Value Problem for a Model of Nonisothermal Flows of a Non-Newtonian Fluid
Anastasia A. Domnich, Mikhail Anatolievich Artemov, Olga Yu. Shishkina · Journal of Applied and Industrial Mathematics · 2020
Under study is some stationary model describing non-Newtonian fluid flows with the viscosity dependent on the strain rate and the heat transfer in a bounded 3D domain. The model is a strongly nonlinear system of coupled partial differential equations for the velocity field, temperature, and pressure. The system is supplemented with a no-slip condition and a linear Robin-type boundary condition for the temperature on the boundary of the flow domain. We propose an operator formulation of this boundary-value problem. Using the properties of d -monotone operators and the Leray-Schauder Fixed Point Theorem, we prove the existence of weak solutions under natural conditions on the data of the model. The solution set is shown to be bounded and closed.