Study of the asymptotic analysis of non-newtonian flow models under boundary conditions formulated in variable-exponent sobolev frameworks

Abstract

In this Masters thesis, we investigate the asymptotic behavior of a Herschel-Bulkley fluid , assumed to be stationary, incompressible, and isothermal, within a bounded three-dimensional domain. The model incorporates a perturbation term of the for muu and is subject to various boundary conditions, all studied in the framework of variable-exponent Sobolev spaces. After introducing the variational formulation, we apply a scaling transformation of The type z=x3, ε which converts the original ε-dependent domain in to a fixed geometric configuration. This transformation enables us to derive a priori estimates for the velocity and pres-sure, and to establish an appropriate convergence result. The work concludes with the analysis of the associated limit problem obtained as ε→0, for which the uniqueness of the solution is demonstrated.