Bingham type fluids with Tresca law in 3D: Existence, Asymptotic analysis, Reynolds equation

  • Rachid Lmangad
  • Faiz Zakaria
  • Hicham BENAISSA FP of Khouribga, Sultan Moulay Slimane University
DOI: https://doi.org/10.19139/soic-2310-5070-2555
Keywords: 3D-asymptotic analysis, Variational inequalities, Bingham type fluid, Tresca law, Reynolds equation

Abstract

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.
Published
2025-06-13
How to Cite
Lmangad, R., Zakaria, F., & BENAISSA, H. (2025). Bingham type fluids with Tresca law in 3D: Existence, Asymptotic analysis, Reynolds equation. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-2555
Issue
Online First
Section
I2CEAI24
Authors who publish with this journal agree to the following terms:

    1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
    2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
    3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).