ON THE ROLE OF THE STOKES PROBLEM IN SECOND GRADE FLUID FLOW IN REGIONS WITH PERMEABLE INTERFACES

Authors

  • R. Maritz University of South Africa - Department of Mathematical Sciences
  • J.M.W. Munganga University of South Africa - Department of Mathematical Sciences

Keywords:

Stokes problem, Helmholtz projection, weak solution, non-Newtonian fluids, permeable boundary, dynamic boundary conditions, kinematic boundary condition

Abstract

The role of the Stokes problem in conducting a theory of existence of solutions, weak as well as classical, is under investigation in this research paper.  We model the motion of incompressible flows of non-Newtonian fluids through permeable boundaries in terms of the Stokes equation.  The equation of motion in the region Ω ∈ \(\mathbb{R}\)3 is coupled with the dynamic boundary condition through the permeable boundary Γ, in order to design a transport equation in a product space Ym.  The existence of a unique solution for the Stokes problem is proved by using a special Helmholtz projection and employing the results from a paper of Agmon et al [1, Theorem 10.5 p.78].  The modelling is done for a special case where a ”shear flow” is assumed.

Cover of n°40 Italian Journal of Pure and Applied Mathematics

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Published

2018-07-31

How to Cite

Maritz, R., & Munganga, J. (2018). ON THE ROLE OF THE STOKES PROBLEM IN SECOND GRADE FLUID FLOW IN REGIONS WITH PERMEABLE INTERFACES. Italian Journal of Pure and Applied Mathematics, 40, 47–60. Retrieved from https://journals.uniurb.it/index.php/ijpam/article/view/7060

Issue

N°40 - July 2018

Section

Articoli - Forum Editrice

License

Copyright (c) 2018 R. Maritz, J.M.W. Munganga

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

L'opera è pubblicata sotto  Licenza Creative Commons Attribuzione 4.0 Internazionale (CC-BY)