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Strip deformation problem in three models of hydrodynamics

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Abstract

We study the problem of a deformation of a straight strip bounded by an impermeable solid wall and a parallel free boundary. Three models of an incompressible fluid are considered: ideal fluid, classical viscous fluid, and dilute solution of a polymer. The influence of the viscous and relaxation factors on the qualitative pattern of fluid motion is revealed.

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Notes

  1. We use the commonly accepted notation for the Hölder classes: \(C^{2+\alpha } [0,1]\) denotes a set of functions \(f(y)\) that are continuous together with their first and second derivatives on the segment \([0,1]\); moreover, \(f''(y)\) satisfies the Hölder condition with the index \(\alpha\); \(C^{2+\alpha, 1+\alpha /2} [\bar{\omega }_{T} ]\) is used to denote the set of functions \(g(y,t)\) that are continuous together with their first and second derivatives with respect to \(y\) and the first derivative with respect to \(t\) in the domain \(\bar{\omega }_{T} \); moreover, \(g_{yy} \) and \(g_{t} \) satisfy the Hölder condition with respect to \(y\) and \(t\) with the respective indices \(\alpha \) and \(\alpha /2\).

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Acknowledgments

The author is grateful to the referee for the valuable comments.

Funding

This study was supported by the Russian Foundation for Basic Research (grant No. 19-01-00096).

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Authors and Affiliations

  1. Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia

    V. V. Pukhnachev

  2. Novosibirsk State University, Novosibirsk, Russia

    V. V. Pukhnachev

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  1. V. V. Pukhnachev
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Correspondence to V. V. Pukhnachev.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2022, Vol. 211, pp. 306–318 https://doi.org/10.4213/tmf10232.

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Pukhnachev, V.V. Strip deformation problem in three models of hydrodynamics. Theor Math Phys 211, 701–711 (2022). https://doi.org/10.1134/S0040577922050105

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