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Shear Hele-Shaw flows of a weakly compressible liquid

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Abstract

We derive an integro-differential system of equations to describe the shear flows of a weakly compressible multicomponent liquid in a Hele-Shaw cell. The velocities of propagation of nonlinear disturbances in the liquid are determined, and the characteristic form of the system is calculated. The conditions for hyperbolicity of the model are formulated that are necessary for the correct statement of the Cauchy problem. The multilayered one-dimensional motion of the liquid are considered and, within the framework of the two-layered scheme of the flow, interpretation is given of the Saffman-Taylor instability.

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Authors and Affiliations

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

    Yu. A. Medova & A. A. Chesnokov

  2. Lavrent’ev Institute of Hydrodynamics, pr. Akad. Lavrent’eva 15, Novosibirsk, 630090, Russia

    Yu. A. Medova & A. A. Chesnokov

Authors
  1. Yu. A. Medova
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  2. A. A. Chesnokov
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Correspondence to A. A. Chesnokov.

Additional information

Original Russian Text © Yu.A. Medova, A.A. Chesnokov, 2014, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2014, Vol. XVII, No. 4, pp. 67–78.

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Medova, Y.A., Chesnokov, A.A. Shear Hele-Shaw flows of a weakly compressible liquid. J. Appl. Ind. Math. 9, 88–97 (2015). https://doi.org/10.1134/S199047891501010X

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  • DOI: https://doi.org/10.1134/S199047891501010X

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