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Solvability of the Initial-Boundary Value Problem for the High-Order Oldroyd Model

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Abstract

In this paper we consider the solvability in the weak sense of the initial-boundary value problem for the high-order Oldroyd model. For the considered model through the Laplace transform, from the rheological relation, the stress tensor is expressed. After its substitution into the motion equations, the initial-boundary value problem is obtained for an integro-differential equation with a memory along trajectories of the velocity field. After that, through the approximating–topological approach to the study of hydrodynamic problems, the existence of a weak solution is proved. In the proof of the assertions, properties of regular Lagrangian flows are essentially used.

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Funding

This work was supported by the Russian Science Foundation (grant no. 22-11-00103).

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Authors and Affiliations

  1. Voronezh State University, 394018, Voronezh, Russia

    V. G. Zvyagin, V. P. Orlov & M. V. Turbin

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  1. V. G. Zvyagin
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  2. V. P. Orlov
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  3. M. V. Turbin
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Correspondence to V. G. Zvyagin, V. P. Orlov or M. V. Turbin.

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Translated by L. Kartvelishvili

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Zvyagin, V.G., Orlov, V.P. & Turbin, M.V. Solvability of the Initial-Boundary Value Problem for the High-Order Oldroyd Model. Russ Math. 66, 70–75 (2022). https://doi.org/10.3103/S1066369X2207009X

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  • DOI: https://doi.org/10.3103/S1066369X2207009X

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