Bingham type fluids with Tresca law in 3D: Existence, Asymptotic analysis, Reynolds equation - Lmangad, Rachid; Zakaria, Faiz; BENAISSA, Hicham (Statistics, Optimization & Information Computing, 2025)
In this work, we study a model for incompressible Bingham fluids in a confined three-dimensional domain, Ωε, where Tresca boundary conditions are applied on part of the boundary and Dirichlet conditions on another. The domain is perturbed by a small parameter ε > 0. We prove the unique solvability of the problem and carry out an asymptotic analysis as one dimension of the fluid domain diminishes to zero. This approach enables the strong convergence of the velocity field, the derivation of a Reynolds-type limit equation, and the analysis of the asymptotic behavior of the Tresca boundary conditions, while rigorously establishing the uniqueness of the limiting velocity and pressure fields.