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On Flows of Bingham-Type Fluids with Threshold Slippage

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  • Evgenii S. Baranovskii

Abstract

We investigate a mathematical model describing 3D steady-state flows of Bingham-type fluids in a bounded domain under threshold-slip boundary conditions, which state that flows can slip over solid surfaces when the shear stresses reach a certain critical value. Using a variational inequalities approach, we suggest the weak formulation to this problem. We establish sufficient conditions for the existence of weak solutions and provide their energy estimates. Moreover, it is shown that the set of weak solutions is sequentially weakly closed in a suitable functional space.

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  • Evgenii S. Baranovskii, 2017. "On Flows of Bingham-Type Fluids with Threshold Slippage," Advances in Mathematical Physics, Hindawi, vol. 2017, pages 1-6, December.
    • Handle: RePEc:hin:jnlamp:7548328
    DOI: 10.1155/2017/7548328
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    Cited by:

    1. Evgenii S. Baranovskii & Olga Yu. Shishkina, 2024. "Generalized Boussinesq System with Energy Dissipation: Existence of Stationary Solutions," Mathematics, MDPI, vol. 12(5), pages 1-15, March.
    2. Amzad Hossain & Md. Mamun Molla & Md. Kamrujjaman & Muhammad Mohebujjaman & Suvash C. Saha, 2023. "MHD Mixed Convection of Non-Newtonian Bingham Nanofluid in a Wavy Enclosure with Temperature-Dependent Thermophysical Properties: A Sensitivity Analysis by Response Surface Methodology," Energies, MDPI, vol. 16(11), pages 1-39, May.
    3. Uzak Zhapbasbayev & Timur Bekibayev & Maksim Pakhomov & Gaukhar Ramazanova, 2024. "Numerical Modeling of Non-Isothermal Laminar Flow and Heat Transfer of Paraffinic Oil with Yield Stress in a Pipe," Energies, MDPI, vol. 17(9), pages 1-20, April.

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