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An Alpha-Model of Polymer Solutions Motion

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Abstract

In this paper, we study the initial–boundary value problem for an alpha-model, which describes the motion of weakly concentrated aqueous polymer solutions. We consider the mathematical model with a rheological relation, satisfying the objectivity principle. On the base of the topological approximation approach for studying hydrodynamic problems, we prove the existence of weak solutions to the alpha-model. We also demonstrate that solutions to the alpha-model converge to the solution of the original model as the value of the parameter alpha tends to zero.

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Funding

This work was supported by the Russian Foundation for Basic Research (grant no. 19–31–60014) and the Ministry of Science and Higher Education of the Russian Federation (the state assignment in the field of science, theme no. FZGU–2020–0035).

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Authors and Affiliations

  1. Voronezh State Pedagogical University, 86 Lenin str., 394043, Voronezh, Russia

    A. V. Zvyagin

  2. Voronezh State University, 1 Universitetskaya sq., 394018, Voronezh, Russia

    A. V. Zvyagin

Authors
  1. A. V. Zvyagin
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Correspondence to A. V. Zvyagin.

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Dedicated to the 90th anniversary of Yuri Grigor’evich Borisovich

Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 5, pp. 33–42.

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Zvyagin, A.V. An Alpha-Model of Polymer Solutions Motion. Russ Math. 65, 21–29 (2021). https://doi.org/10.3103/S1066369X21050054

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  • DOI: https://doi.org/10.3103/S1066369X21050054

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