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Symmetries in equations of incompressible viscoelastic Maxwell medium*

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Abstract

We consider unsteady flows of incompressible viscoelastic Maxwell medium with upper, low, and Jaumann convective derivatives in the rheological constitutive law. We give characteristics of a system of equations that describe a three-dimensional motion of such a medium for all three types of convective derivative. In the general case, due to the incompressibility condition, the equations of motion have both real and complex characteristics. We study group properties of this system in the two-dimensional case. On this basis, we choose submodels of the Maxwell model that can be reduced to hyperbolic ones. The properties of the hyperbolic submodels obtained depend on the choice of the invariant derivative in the rheological relation. We also present concrete examples of invariant solutions.

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Authors and Affiliations

  1. Lavrentyev Institute of Hydrodynamics of the Siberian Branch of the RAS, 630090, Novosibirsk, 15 acad. Lavrentyev ave., Russia

    Vladislav V. Pukhnachev & Elena Yu. Fominykh

  2. Novosibirsk State University, 630090, Novosibirsk, 1 Pirogova str., Russia

    Vladislav V. Pukhnachev

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  1. Vladislav V. Pukhnachev
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  2. Elena Yu. Fominykh
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Correspondence to Vladislav V. Pukhnachev.

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* This work was carried out with the support of a RFBR grant (No. 16-01-00127).

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Pukhnachev, V.V., Fominykh, E.Y. Symmetries in equations of incompressible viscoelastic Maxwell medium*. Lith Math J 58, 309–319 (2018). https://doi.org/10.1007/s10986-018-9401-8

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  • DOI: https://doi.org/10.1007/s10986-018-9401-8

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