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On Solvability of a Fluid Flow Alpha-Model With Memory

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Abstract

We study weak solvability of an alpha-model in non-Newtonian hydrodynamics. If the parameter alpha equals zero, then the alpha-model coincides with the classical one describing a fluid flow with memory. This model takes into account fluid’s memory along trajectories of movement. Additionally, we show that solutions of the alpha-model tend to solutions to the classical model as the parameter alpha tends to zero.

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Authors and Affiliations

  1. Peoples Friendship University of Russia, ul. Miklukho-Maklaya 6, Moscow, 117198, Russia

    A. V. Zvyagin

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

    A. V. Zvyagin & V. G. Zvyagin

  3. Southern Mathematical Institute, Vladikavkaz Scientific Center of Russian Academy of Sciences, ul. Markusa 22, Vladikavkaz, 362027, Russia

    D. M. Polyakov

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

    D. M. Polyakov

Authors
  1. A. V. Zvyagin
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  2. V. G. Zvyagin
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  3. D. M. Polyakov
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Correspondence to A. V. Zvyagin.

Additional information

Original Russian Text © A.V. Zvyagin, V.G. Zvyagin, D.M. Polyakov, 2018, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2018, No. 6, pp. 78–84.

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Zvyagin, A.V., Zvyagin, V.G. & Polyakov, D.M. On Solvability of a Fluid Flow Alpha-Model With Memory. Russ Math. 62, 69–74 (2018). https://doi.org/10.3103/S1066369X18060075

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  • DOI: https://doi.org/10.3103/S1066369X18060075

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