On the strong convergence of the solution of a generalized non-Newtonian fluid with Coulomb law in a thin film

Hana Taklit Lahlah; Hamid Benseridi; Bahri Cherif; Mourad Dilmi; Salah Boulaaras; Rabab Alharbi; Hana Taklit Lahlah; Hamid Benseridi; Bahri Cherif; Mourad Dilmi; Salah Boulaaras; Rabab Alharbi

doi:10.3934/math.2023635

AIMS Mathematics

2023, Volume 8, Issue 6: 12637-12656. doi: 10.3934/math.2023635

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Research article

On the strong convergence of the solution of a generalized non-Newtonian fluid with Coulomb law in a thin film

1.
Applied Mathematics Laboratory, Department of Mathematics, Faculty of Sciences, University of Ferhat ABBAS- Sétif 1, 19000, Algeria
2.
Department of Mathematics, College of Science and Arts at ArRass, Qassim University, Qassim, Saudi Arabia

Received: 12 December 2022 Revised: 02 March 2023 Accepted: 06 March 2023 Published: 29 March 2023
MSC : 35R35, 76F10, 78M35, 35B40, 35J85

The goal of this paper is to examine the strong convergence of the velocity of a non-Newtonian incompressible fluid whose viscosity follows the power law with Coulomb friction. We assume that the fluid coefficients of the thin layer vary with respect to the thin layer parameter $ \varepsilon $. We give in a first step the description of the problem and basic equations. Then, we present the functional framework. The following paragraph is reserved for the main convergence results. Finally, we give the detail of the proofs of these results.
- mathematical operators,
- partial differential equations,
- Coulomb law,
- non-Newtonian fluid,
- weak generalized equation,
- variational inequality
Citation: Hana Taklit Lahlah, Hamid Benseridi, Bahri Cherif, Mourad Dilmi, Salah Boulaaras, Rabab Alharbi. On the strong convergence of the solution of a generalized non-Newtonian fluid with Coulomb law in a thin film[J]. AIMS Mathematics, 2023, 8(6): 12637-12656. doi: 10.3934/math.2023635

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Abstract

The goal of this paper is to examine the strong convergence of the velocity of a non-Newtonian incompressible fluid whose viscosity follows the power law with Coulomb friction. We assume that the fluid coefficients of the thin layer vary with respect to the thin layer parameter $ \varepsilon $. We give in a first step the description of the problem and basic equations. Then, we present the functional framework. The following paragraph is reserved for the main convergence results. Finally, we give the detail of the proofs of these results.

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