Solvability of the Boussinesq Approximation for Water Polymer Solutions

Mikhail A. Artemov and Evgenii S. Baranovskii
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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

Mathematics, 2019, vol. 7, issue 7, 1-10

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.

Keywords: boundary-value problem; existence theorem; weak solutions; Boussinesq equations; heat transfer; water polymer solutions; second-grade fluids; slip boundary condition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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