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A Well-Posed Boundary Value Problem for Supercritical Flow of Viscoelastic Fluids of Maxwell Type

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Nonlinear Evolution Equations That Change Type

Part of the book series: The IMA Volumes in Mathematics and Its Applications ((IMA,volume 27))

Abstract

For a class of viscoelastic fluids with differential constitutive laws of Maxwell type, we investigate the existence and uniqueness of steady flows. We consider small perturbations of uniform flow transverse to a strip. A well-posed boundary value problem is formulated for the case when the velocity of the fluid exceeds the speed of propagation of shear waves.

This research was completed while I was visiting the Institute for Mathematics and its Applications at the University of Minnesota. Financial support from the IMA and from the National Science Foundation under Grant No. DMS-8796241 is gratefully acknowledged.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics and ICAM, Virginia Tech, Blacksburg, VA, 24061-0123, USA

    Michael Renardy

Authors
  1. Michael Renardy
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Houston, Houston, Texas, 77204, USA

    Barbara Lee Keyfitz

  2. Department of Mathematics, North Carolina State University, Raleigh, North Carolina, 27695, USA

    Michael Shearer

Additional information

This paper is dedicated to Daniel D. Joseph on the occasion of his 60th birthday

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© 1990 Springer-Verlag New York Inc.

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Renardy, M. (1990). A Well-Posed Boundary Value Problem for Supercritical Flow of Viscoelastic Fluids of Maxwell Type. In: Keyfitz, B.L., Shearer, M. (eds) Nonlinear Evolution Equations That Change Type. The IMA Volumes in Mathematics and Its Applications, vol 27. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9049-7_14

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  • DOI: https://doi.org/10.1007/978-1-4613-9049-7_14

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-9051-0

  • Online ISBN: 978-1-4613-9049-7

  • eBook Packages: Springer Book Archive

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