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Hyperbolicity and change of type in the flow of viscoelastic fluids

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Abstract

The equations governing the flow of viscoelastic liquids are classified according to the symbol of their differential operators. Propagation of singularities is discussed and conditions for a change of type are investigated. The vorticity equation for steady flow can change type when a critical condition involving speed and stresses is satisfied. This leads to a partitioning of the field of flow into subcritical and supercritical regions, as in the problem of transonic flow.

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Authors and Affiliations

  1. Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis

    Daniel D. Joseph, Michael Renardy & Jean-Claude Saut

  2. Department of Mathematics and Mathematics Research Center, University of Wisconsin, Madison

    Daniel D. Joseph, Michael Renardy & Jean-Claude Saut

  3. Department of Mathematics, Université de Paris-Sud, Orsay

    Daniel D. Joseph, Michael Renardy & Jean-Claude Saut

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  1. Daniel D. Joseph
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  2. Michael Renardy
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  3. Jean-Claude Saut
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Dedicated to Walter Noll on the Occasion of his 60th Birthday

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Joseph, D.D., Renardy, M. & Saut, JC. Hyperbolicity and change of type in the flow of viscoelastic fluids. Arch. Rational Mech. Anal. 87, 213–251 (1985). https://doi.org/10.1007/BF00250725

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  • DOI: https://doi.org/10.1007/BF00250725

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