Non-uniqueness and linear stability of the one-dimensional flow of multiple viscoelastic fluids

Hervé Le Meur

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1997)

  • Volume: 31, Issue: 2, page 185-211
  • ISSN: 0764-583X

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Le Meur, Hervé. "Non-uniqueness and linear stability of the one-dimensional flow of multiple viscoelastic fluids." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 31.2 (1997): 185-211. <http://eudml.org/doc/193835>.

@article{LeMeur1997,
author = {Le Meur, Hervé},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Poiseuille flow; Phan-Thien Tanner model; modified Phan-Thien Tanner model; Couette flow},
language = {eng},
number = {2},
pages = {185-211},
publisher = {Dunod},
title = {Non-uniqueness and linear stability of the one-dimensional flow of multiple viscoelastic fluids},
url = {http://eudml.org/doc/193835},
volume = {31},
year = {1997},
}

TY - JOUR
AU - Le Meur, Hervé
TI - Non-uniqueness and linear stability of the one-dimensional flow of multiple viscoelastic fluids
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1997
PB - Dunod
VL - 31
IS - 2
SP - 185
EP - 211
LA - eng
KW - Poiseuille flow; Phan-Thien Tanner model; modified Phan-Thien Tanner model; Couette flow
UR - http://eudml.org/doc/193835
ER -

References

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  1. [1] C. GUILLOPÉ & J. C. SAUT, 1990, "Global existence and one-dimensional non linear stabihty of shearing motions of viscoelastic fluids of Oldroyd type", M2AN Vol 24, n° 3, 369-401. Zbl0701.76011MR1055305
  2. [2] R. W. KOLKKA, G. R. IERLEY, M. G. HANSEN & R. A. WORTHING, 1987, "On the stability of viscoelastic parallel shear flows", Technical Report, F.R.O.G. Michigan Technological University. 
  3. [3] C. GUILLOPÉ & J. C. SAUT, 1990, "Existence results for the flow of viscoelastic fluids with a differential constitutive law". Nonlinear Analysis Theory, Methods & Applications, Vol. 15, No 9, 849-869. Zbl0729.76006MR1077577
  4. [4] R. J. GORDON & SCHOWALTER, 1972, Trans. Soc. Rheol., 16, 79. Zbl0368.76006
  5. [5] L. A. DÀVALOS-OROZCO, 1992, "Capillary instability due to a shear stress on the free surface of a viscoelastic fluid layer", J. Non-Newtonian Fluid Mech., 45, 171-186. Zbl0761.76021
  6. [6] M. RENARDY & Y. RENARDY, 1986, "Linear stability of plane Couette flow of an Upper Convected Maxwell fluid", J. Non-Newtonian Fluid Mech., 22, 23-33. Zbl0608.76006
  7. [7] G. M. WILSON & B. KHOMAMI, 1992, "An experimental investigation of interfacial instabilities in multilayer flow of viscoelastic fluids. I. Incompatible polymer Systems", J. Non-Newtonian Fluid Mech., 45, 355-384. 
  8. [8] H. LE MEUR, 1994, Existence, unicité et stabilité d'écoulements de fluides viscoélastiques avec interface, PhD Thesis of University Paris-Sud Orsay. 
  9. [9] D. D. JOSEPH, Fluid dynamics of Visco Elastic liquids, Applied Mathematical Sciences 84 Springer Verlag. Zbl0698.76002MR1051193
  10. [10] D. D. JOSEPH, 1976, Stability of fluid motions, Vol. I, II Springer. Zbl0345.76023
  11. [11] N. PHAN-THIEN & R. I. TANNER, 1977, "A new constitutive equation derived from network theory", J. Non-Newtonian Fluid Mech, 2, 353-365. Zbl0361.76011
  12. [12] R. I. TANNER, Viscoélasticité non linéaire : Rhéologie et modélisation numérique, Ecoles CEA-EDF-INRIA, 27-30/01/ 1992. 
  13. [13] R. KEUNINGS & M. J. CROCHET, 1984, "Numerical simulation of the flow of a viscoelastic fluid through an abrupt contraction", J. Non Newtonian Fluid Mech., 14, 279 299. Zbl0531.76013
  14. [14] M. RENARDY, "On the linear stability of parallel shear flows of viscoelastic fluids of Jeffreys type". to appear. 
  15. [15] M. RENARDY, 1993, "On the type of certain C0 Semigroups", Comm. Part. Diff. Eq., 18 (7 & 8), 1299-1307. Zbl0801.47029MR1233196
  16. [16] P. HENRICI, 1974, Applied and Computational Complex Analysis, vol. I, John Wiley, New-York. Zbl0313.30001MR372162

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