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Strong Solutions of the Incompressible Navier–Stokes–Voigt Model

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  • Evgenii S. Baranovskii

    (Department of Applied Mathematics, Informatics and Mechanics, Voronezh State University, 394018 Voronezh, Russia)

Abstract

This paper deals with an initial-boundary value problem for the Navier–Stokes–Voigt equations describing unsteady flows of an incompressible non-Newtonian fluid. We give the strong formulation of this problem as a nonlinear evolutionary equation in Sobolev spaces. Using the Faedo–Galerkin method with a special basis of eigenfunctions of the Stokes operator, we construct a global-in-time strong solution, which is unique in both two-dimensional and three-dimensional domains. We also study the long-time asymptotic behavior of the velocity field under the assumption that the external forces field is conservative.

Suggested Citation

  • Evgenii S. Baranovskii, 2020. "Strong Solutions of the Incompressible Navier–Stokes–Voigt Model," Mathematics, MDPI, vol. 8(2), pages 1-16, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:181-:d:315696
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    References listed on IDEAS

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    1. Mikhail A. Artemov & Evgenii S. Baranovskii, 2019. "Solvability of the Boussinesq Approximation for Water Polymer Solutions," Mathematics, MDPI, vol. 7(7), pages 1-10, July.
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    Cited by:

    1. Alyona Zamyshlyaeva & Aleksandr Lut, 2021. "Inverse Problem for the Sobolev Type Equation of Higher Order," Mathematics, MDPI, vol. 9(14), pages 1-13, July.
    2. Evgenii S. Baranovskii & Mikhail A. Artemov & Sergey V. Ershkov & Alexander V. Yudin, 2025. "The Kelvin–Voigt–Brinkman–Forchheimer Equations with Non-Homogeneous Boundary Conditions," Mathematics, MDPI, vol. 13(6), pages 1-18, March.

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