Some theoretical results concerning non newtonian fluids of the Oldroyd kind
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 26 (1998) no. 1, p. 1-29
@article{ASNSP_1998_4_26_1_1_0,
     author = {Fern\'andez-Cara, Enrique and Guill\'en, Francisco and Ortega, Rubens R.},
     title = {Some theoretical results concerning non newtonian fluids of the Oldroyd kind},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 26},
     number = {1},
     year = {1998},
     pages = {1-29},
     zbl = {0914.76006},
     mrnumber = {1633055},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1998_4_26_1_1_0}
}
Fernández-Cara, Enrique; Guillén, Francisco; Ortega, Rubens R. Some theoretical results concerning non newtonian fluids of the Oldroyd kind. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 26 (1998) no. 1, pp. 1-29. http://www.numdam.org/item/ASNSP_1998_4_26_1_1_0/

[1] G. Astarita - G. Marrucci, "Principles of Non-Newtonian Fluid Mechanics", McGraw Hill, New York, 1974.

[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. | MR 1182509 | Zbl 0761.76032

[3] M.J. Crochet - A.R. Davies - K. Walters, "Numerical Simulation of Non-Newtonian Flow", Elsevier, Amsterdam, 1985. | MR 801545 | Zbl 0583.76002

[4] R. Diperna - P.-L. Lions, Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math. 98 (1989), 511-547. | MR 1022305 | Zbl 0696.34049

[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. | MR 1289322 | Zbl 0808.76005

[6] A. Friedman, "Partial Differential Equations", Holt- Rinehart-Winston, New York, 1976. | MR 454266 | Zbl 0224.35002

[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. Acta 21 (1982), 366-375. | Zbl 0513.76009

[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. | MR 1138838 | Zbl 0739.35067

[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. | MR 1077577 | Zbl 0729.76006

[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. | Numdam | MR 1055305 | Zbl 0701.76011

[11] O.A. Ladyzhenskaya, "The Mathematical Theory of Viscous Incompressible Flow", Gordon and Breach, New York, 1969. | MR 254401 | Zbl 0184.52603

[12] R.G. Larson, A critical comparison of constitutive equations for polymer melts, J. Non-Newtonian Fluid Mech. 23 (1987), 249-269.

[13] J. Leray, Sur le mouvement d'une liquide visqueux emplissant l'espace, Acta Math. 63 (1934), 193-248. | JFM 60.0726.05

[14] J.L. Lions, "Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires ", Dunod, Gauthier-Villars, Paris, 1969. | MR 259693 | Zbl 0189.40603

[15] J.G. Oldroyd, On the formulation of rheological equations of state, Proc. Roy. Soc. London Ser. A 200 (1950), 523-541. | MR 35192 | Zbl 1157.76305

[16] J.G. Oldroyd, Non-Newtonian effects in steady motion of some idealized elastico-viscous liquids, Proc. Roy. Soc. London Ser. A 245 (1958), 278-297. | MR 94085 | Zbl 0080.38805

[17] R.R. Ortega, Thesis, University of Seville (Spain), 1995.

[18] N. Phan Thien - R.I. Tanner, A new constitutive equation derived from network theory, J. Non-Newtonian Fluid Mech. 2 (1977), 353-365. | Zbl 0361.76011

[19] M Renardy, Existence of slow flows of viscoelastic fluids with differential constitutive equations, Z. Angew. Math. Mech. 65 (1985), 449-451. | MR 814684 | Zbl 0577.76014

[20] M. Renardy - W.J. Hrusa - J.A. Nohel, "Mathematical Problems in Viscoelasticity", Longman, London, 1987. | MR 919738 | Zbl 0719.73013

[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. | MR 1119920 | Zbl 0737.76048

[22] R. Témam, "Navier-Stokes Equations, Theory and Numerical Analysis", North-Holland, Amsterdam, 1977. | MR 609732 | Zbl 0383.35057

[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. | Numdam | MR 753158 | Zbl 0542.35062

[24] A. Valli, Navier-Stokes equations for compressible fluids: global estimates and periodic solutions, Proc. Sympos Pure Math. 45 (1986), 467-478. | MR 843633 | Zbl 0601.35094

[25] K. WALTERS (ed.), "Rheometry: Industrial Applications", J. Wiley and Sons, 1980.