Study of the stationary solution of non-isothermal Bingham flow

Abstract

This research investigates the asymptotic behavior of a stationary, non-isothermal Bingham fluid flow in a three-dimensional thin domain Ωε associated with nonlinear Tresca friction conditions. By applying a scaling technique, the problem is transformed from the thin domain depending on the parameter ε into a fixed reference domain Ωindependent of this parameter (which represents the layer thickness tending to zero). Uniform a priori estimates are established, and the convergence of the unknowns—namely velocity, pressure, and temperature—is analyzed. Finally, the limit problem is proven, and the general two-dimensional Reynolds equation is derived as a simplified and accurate model for industrial applications.