Global existence and one-dimensional nonlinear stability of shearing motions of viscoelastic fluids of Oldroyd type
ESAIM: Modélisation mathématique et analyse numérique, Tome 24 (1990) no. 3, pp. 369-401. 
@article{M2AN_1990__24_3_369_0,
     author = {Guillop\'e, C. and Saut, J.-C.},
     title = {Global existence and one-dimensional nonlinear stability of shearing motions of viscoelastic fluids of {Oldroyd} type},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {369--401},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {24},
     number = {3},
     year = {1990},
     mrnumber = {1055305},
     zbl = {0701.76011},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1990__24_3_369_0/}
}
TY  - JOUR
AU  - Guillopé, C.
AU  - Saut, J.-C.
TI  - Global existence and one-dimensional nonlinear stability of shearing motions of viscoelastic fluids of Oldroyd type
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 1990
SP  - 369
EP  - 401
VL  - 24
IS  - 3
PB  - AFCET - Gauthier-Villars
PP  - Paris
UR  - http://www.numdam.org/item/M2AN_1990__24_3_369_0/
LA  - en
ID  - M2AN_1990__24_3_369_0
ER  - 
%0 Journal Article
%A Guillopé, C.
%A Saut, J.-C.
%T Global existence and one-dimensional nonlinear stability of shearing motions of viscoelastic fluids of Oldroyd type
%J ESAIM: Modélisation mathématique et analyse numérique
%D 1990
%P 369-401
%V 24
%N 3
%I AFCET - Gauthier-Villars
%C Paris
%U http://www.numdam.org/item/M2AN_1990__24_3_369_0/
%G en
%F M2AN_1990__24_3_369_0
Guillopé, C.; Saut, J.-C. Global existence and one-dimensional nonlinear stability of shearing motions of viscoelastic fluids of Oldroyd type. ESAIM: Modélisation mathématique et analyse numérique, Tome 24 (1990) no. 3, pp. 369-401. http://www.numdam.org/item/M2AN_1990__24_3_369_0/

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

[2] C. Guillopé, J. C. Saut, Résultats d'existence pour des fluides viscoélastiques à loi de comportement de type différentiel. C.R. Acad. Sci. Paris, 305, série I (1987), 489-492, and article to appear in Nonlinear An., T.M.A. | MR | Zbl

[3] P. Henrici, Applied and Computational Complex Analysis, vol. I, John Wiley, New York, 1974. | MR | Zbl

[4] G. Iooss, Bifurcation et stabilité, Publications Mathématiques d'Orsay, 1973. | MR

[5] D. D. Joseph, Stability of Fluid Motions, vol. I and II, Springer, Berlin-Heidelberg-New York, 1976. | Zbl

[6] T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin-Heidel-berg-New York, 1966. | MR | Zbl

[7] R. W. Kolkka, G. R. Ierley, M. G. Hansen,R. A. Worthing, On the stability of viscoelastic parallel shear flows, Technical Report, F.R.O.G., Michigan Technological University, 1987.

[8] R. W. Kolkka, D. S. Malkus, M. G. Hansen,G. R. Ierley, R. A. Worthing, Spurt phenomena of the Johnson-Segalman fluid and related models, J. Non-Newt. Fl. Mech., 29 (1988), 303-335.

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

[10] G. Prodi, Theoremi di tipo locale per il sistema di Navier-Stokes e la stabilita delle soluzione stazionarie, Rend. Sem. Univ. Padova, 32 (1962), 374-397. | Numdam | MR | Zbl

[11] M. Renardy, W. J. Hrusa, J. A. Nohel, Mathematical Problems in Viscoelasticity, Longman, New York, 1987. | MR | Zbl

[12] D. H. Sattinger, Topics in Stability and Bifurcation Theory, Lectures Notes in Mathematics, 309, Springer, Berlin-Heidelberg-New York, 1973. | MR | Zbl

[13] W. R. Schowalter, Behavior of complex fluids at solid boundaries, J. Non-Newt. Fl. Mech., 29 (1988), 85.

[14] J. Yerushalmi, S. Katz, R. Shinnar, The stability of steady shear flows of some viscoelastic fluids, Chem. Eng. Sc., 25 (1970), 1891-1902.

[15] J. K. Hunter, M. Slemrod, Viscoelastic fluid flow exhibiting hysteritic phase changes, Phys. Fluids 26 (1983), 2345-2351. | Zbl

[16] D. S. Malkus, J. A. Nohel, B. J. Plohr, Time-dependent shear flow of a non-Newtonian fluid, in Contemporary Mathematics, vol. 100, ed. W. B. Lindquist, A.M.S. (1989), 91-110. | MR | Zbl