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Solvability of the Boussinesq Approximation for Water Polymer Solutions

Author

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  • Mikhail A. Artemov

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

  • Evgenii S. Baranovskii

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

Abstract

We consider nonlinear Boussinesq-type equations that model the heat transfer and steady viscous flows of weakly concentrated water solutions of polymers in a bounded three-dimensional domain with a heat source. On the boundary of the flow domain, the impermeability condition and a slip condition are provided. For the temperature field, we use a Robin boundary condition corresponding to the classical Newton law of cooling. By using the Galerkin method with special total sequences in suitable function spaces, we prove the existence of a weak solution to this boundary-value problem, assuming that the heat source intensity is bounded. Moreover, some estimates are established for weak solutions.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:7:p:611-:d:247108
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    Cited by:

    1. Evgenii S. Baranovskii, 2020. "Strong Solutions of the Incompressible Navier–Stokes–Voigt Model," Mathematics, MDPI, vol. 8(2), pages 1-16, February.

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