Some theoretical results concerning non newtonian fluids of the Oldroyd kind

Enrique Fernández-Cara; Francisco Guillén; Rubens R. Ortega

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1998)

  • Volume: 26, Issue: 1, page 1-29
  • ISSN: 0391-173X

How to cite


Fernández-Cara, Enrique, Guillén, Francisco, and Ortega, Rubens R.. "Some theoretical results concerning non newtonian fluids of the Oldroyd kind." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 26.1 (1998): 1-29. <>.

author = {Fernández-Cara, Enrique, Guillén, Francisco, Ortega, Rubens R.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {global in time existence; uniqueness; stability},
language = {eng},
number = {1},
pages = {1-29},
publisher = {Scuola normale superiore},
title = {Some theoretical results concerning non newtonian fluids of the Oldroyd kind},
url = {},
volume = {26},
year = {1998},

AU - Fernández-Cara, Enrique
AU - Guillén, Francisco
AU - Ortega, Rubens R.
TI - Some theoretical results concerning non newtonian fluids of the Oldroyd kind
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1998
PB - Scuola normale superiore
VL - 26
IS - 1
SP - 1
EP - 29
LA - eng
KW - global in time existence; uniqueness; stability
UR -
ER -


  1. [1] G. Astarita - G. Marrucci, "Principles of Non-Newtonian Fluid Mechanics", McGraw Hill, New York, 1974. Zbl0316.73001
  2. [2] J. Baranger - D. Sandri, Finite element approximation of viscoelastic fluid flow: Existence of approximate solutions and error bounds, Numer. Math.63 (1992), 13-27. Zbl0761.76032MR1182509
  3. [3] M.J. Crochet - A.R. Davies - K. Walters, "Numerical Simulation of Non-Newtonian Flow", Elsevier, Amsterdam, 1985. Zbl0583.76002MR801545
  4. [4] R. Diperna - P.-L. Lions, Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math.98 (1989), 511-547. Zbl0696.34049MR1022305
  5. [5] E. Fernández-Cara - F. Guillén - R.R. Ortega, Existence et unicité de solution forte locale en temps pour des fluides non newtoniens de type Oldroyd (version LS - Lr), C. R. Acad. Sci. Paris. Sér. I Math.319 (1994), 411-416. Zbl0808.76005MR1289322
  6. [6] A. Friedman, "Partial Differential Equations", Holt- Rinehart-Winston, New York, 1976. Zbl0224.35002MR454266
  7. [7] H. Giesekus, A unified approach to a variety of constitutive models for polymer fluids based on the concept of configuration dependent molecular mobility, Rheol. Acta21 (1982), 366-375. Zbl0513.76009
  8. [8] Y. Giga - H. Sohr, Abstract LP estimates for the Cauchy problem with applications to the Navier-Stokes equations in exterior domains, J. Funct. Anal.102 (1991), 72-94. Zbl0739.35067MR1138838
  9. [9] C. Guillopé - J.-C. Saut, Existence results for the flow of viscoelastic fluids with a differential constitutive law, Nonlinear Anal. Vol. 15, No. 9, (1990), 849-869. Zbl0729.76006MR1077577
  10. [10] C. Guillopé - J.-C. Saut, Global existence and one-dimensional nonlinear stability of shearing motions of viscoelastic fluids of Oldroyd type, Math. Mod. Numer. Anal. Vol. 24, No. 3, (1990), 369-401. Zbl0701.76011MR1055305
  11. [11] O.A. Ladyzhenskaya, "The Mathematical Theory of Viscous Incompressible Flow", Gordon and Breach, New York, 1969. Zbl0184.52603MR254401
  12. [12] R.G. Larson, A critical comparison of constitutive equations for polymer melts, J. Non-Newtonian Fluid Mech.23 (1987), 249-269. 
  13. [13] J. Leray, Sur le mouvement d'une liquide visqueux emplissant l'espace, Acta Math.63 (1934), 193-248. JFM60.0726.05
  14. [14] J.L. Lions, "Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires ", Dunod, Gauthier-Villars, Paris, 1969. Zbl0189.40603MR259693
  15. [15] J.G. Oldroyd, On the formulation of rheological equations of state, Proc. Roy. Soc. London Ser.A200 (1950), 523-541. Zbl1157.76305MR35192
  16. [16] J.G. Oldroyd, Non-Newtonian effects in steady motion of some idealized elastico-viscous liquids, Proc. Roy. Soc. London Ser. A245 (1958), 278-297. Zbl0080.38805MR94085
  17. [17] R.R. Ortega, Thesis, University of Seville (Spain), 1995. 
  18. [18] N. Phan Thien - R.I. Tanner, A new constitutive equation derived from network theory, J. Non-Newtonian Fluid Mech.2 (1977), 353-365. Zbl0361.76011
  19. [19] M Renardy, Existence of slow flows of viscoelastic fluids with differential constitutive equations, Z. Angew. Math. Mech.65 (1985), 449-451. Zbl0577.76014MR814684
  20. [20] M. Renardy - W.J. Hrusa - J.A. Nohel, "Mathematical Problems in Viscoelasticity", Longman, London, 1987. Zbl0719.73013MR919738
  21. [21] D. Sandri, Approximation par éléments finis d'écoulements de fluides viscoélastiques: Existence de solutions approchées et majoration d'erreur II. Contraintes continues, C. R. Acad. Paris Sér. I Math.313 (1991), 111-114. Zbl0737.76048MR1119920
  22. [22] R. Témam, "Navier-Stokes Equations, Theory and Numerical Analysis", North-Holland, Amsterdam, 1977. Zbl0383.35057MR609732
  23. [23] A. Valli, Periodic and stationary solutions for compressible Navier-Stokes equations via a stability method, Ann. Scuola Norm. Sup. Pisa Cl. Sci.10 (1983), 607-647. Zbl0542.35062MR753158
  24. [24] A. Valli, Navier-Stokes equations for compressible fluids: global estimates and periodic solutions, Proc. Sympos Pure Math.45 (1986), 467-478. Zbl0601.35094MR843633
  25. [25] K. WALTERS (ed.), "Rheometry: Industrial Applications", J. Wiley and Sons, 1980. 

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