Global existence and one-dimensional nonlinear stability of shearing motions of viscoelastic fluids of Oldroyd type
- Volume: 24, Issue: 3, page 369-401
- ISSN: 0764-583X
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topGuillopé, C., and Saut, J.-C.. "Global existence and one-dimensional nonlinear stability of shearing motions of viscoelastic fluids of Oldroyd type." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 24.3 (1990): 369-401. <http://eudml.org/doc/193600>.
@article{Guillopé1990,
author = {Guillopé, C., Saut, J.-C.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {shearing; Poiseuille flows; Oldroyd (Johnson-Segalman) fluids; retardation time; stability},
language = {eng},
number = {3},
pages = {369-401},
publisher = {Dunod},
title = {Global existence and one-dimensional nonlinear stability of shearing motions of viscoelastic fluids of Oldroyd type},
url = {http://eudml.org/doc/193600},
volume = {24},
year = {1990},
}
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: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1990
PB - Dunod
VL - 24
IS - 3
SP - 369
EP - 401
LA - eng
KW - shearing; Poiseuille flows; Oldroyd (Johnson-Segalman) fluids; retardation time; stability
UR - http://eudml.org/doc/193600
ER -
References
top- [1] G. ASTARITA, G. MARRUCCI, Principles of Non-Newtonian Fluid Mechanics, McGraw-Hill, London, 1974. Zbl0316.73001
- [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. Zbl0624.76008MR916317
- [3] P. HENRICI, Applied and Computational Complex Analysis, vol. I, John Wiley, New York, 1974. Zbl0313.30001MR372162
- [4] G. IOOSS, Bifurcation et stabilité, Publications Mathématiques d'Orsay, 1973. MR487634
- [5] D. D. JOSEPH, Stability of Fluid Motions, vol. I and II, Springer, Berlin-Heidelberg-New York, 1976. Zbl0345.76023
- [6] T. KATO, Perturbation Theory for Linear Operators, Springer, Berlin-Heidel-berg-New York, 1966. Zbl0148.12601MR203473
- [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. Zbl1157.76305MR35192
- [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. Zbl0108.28602MR189354
- [11] M. RENARDY, W. J. HRUSA, J. A. NOHEL, Mathematical Problems in Viscoelasticity, Longman, New York, 1987. Zbl0719.73013MR919738
- [12] D. H. SATTINGER, Topics in Stability and Bifurcation Theory, Lectures Notes in Mathematics, 309, Springer, Berlin-Heidelberg-New York, 1973. Zbl0248.35003MR463624
- [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. Zbl0529.76009
- [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. Zbl0683.76003MR1033511
Citations in EuDML Documents
top- Hervé Le Meur, Non-uniqueness and linear stability of the one-dimensional flow of multiple viscoelastic fluids
- P. Saramito, A new -scheme algorithm and incompressible FEM for viscoelastic fluid flows
- Enrique Fernández-Cara, Francisco Guillén, Rubens R. Ortega, Some theoretical results concerning non newtonian fluids of the Oldroyd kind
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