Sur une classe de fluides non newtoniens: les solutions aqueuses de polymères
Author:
C. Amrouche
Journal:
Quart. Appl. Math. 50 (1992), 779-791
MSC:
Primary 76A05; Secondary 35Q35, 76D05
DOI:
https://doi.org/10.1090/qam/1193666
MathSciNet review:
MR1193666
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Abstract: The aim of this paper is to study a nonlinear evolution system of third order representing an approximation of Navier-Stokes equations. This system describes the motion of a viscous fluid to which a small quantity of polymers is added. The consequently main relaxation properties of the resulting fluid are completely changed.
C. Amrouche, Thèse de troisième cycle: Etude globale des fluides de troisième grade, Université Paris 6 (1986)
- Chérif Amrouche and Vivette Girault, Une méthode d’approximation mixte des équations des fluides non newtoniens de troisième grade, Numer. Math. 53 (1988), no. 3, 315–349 (French, with English summary). MR 948590, DOI https://doi.org/10.1007/BF01404467
D. Cioranescu and E. H. Ouazar, Existence and uniqueness for fluids of second grade, Non Linear Partial Differential Equations, vol. 109, Collège de France Seminar, Pitman, New York, 1983, pp. 178–197
G. de Rham, Variétés Différentiables, Hermann, Paris, 1960
- Vivette Girault and Pierre-Arnaud Raviart, Finite element methods for Navier-Stokes equations, Springer Series in Computational Mathematics, vol. 5, Springer-Verlag, Berlin, 1986. Theory and algorithms. MR 851383
- J.-L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod; Gauthier-Villars, Paris, 1969 (French). MR 0259693
- A. P. Oskolkov, The uniqueness and solvability in the large of boundary value problems for the equations of motion of aqueous solutions of polymers, Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 38 (1973), 98–136 (Russian). Boundary value problems of mathematical physics and related questions in the theory of functions, 7. MR 0377311
- A. P. Oskolkov, Solvability in the large of the first boundary value problem for a certain quasilinear third order system that is encountered in the study of the motion of a viscous fluid, Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 27 (1972), 145–160 (Russian). Boundary value problems of mathematical physics and related questions in the theory of functions, 6. MR 0328380
- Roger Temam, Navier-Stokes equations, 3rd ed., Studies in Mathematics and its Applications, vol. 2, North-Holland Publishing Co., Amsterdam, 1984. Theory and numerical analysis; With an appendix by F. Thomasset. MR 769654
C. Amrouche, Thèse de troisième cycle: Etude globale des fluides de troisième grade, Université Paris 6 (1986)
C. Amrouche et V. Girault, Une méthode d’approximation mixte des équations de fluides non newtoniens de troisième grade, Numerische Mathematik, vol. 53, Springer-Verlag, Berlin, 1988, pp. 315–349
D. Cioranescu and E. H. Ouazar, Existence and uniqueness for fluids of second grade, Non Linear Partial Differential Equations, vol. 109, Collège de France Seminar, Pitman, New York, 1983, pp. 178–197
G. de Rham, Variétés Différentiables, Hermann, Paris, 1960
V. Girault and P. A. Raviart, Finite Element Methods for Navier-Stokes Equations, Springer-Verlag, Berlin, 1986
J. L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires, Gauthier-Villars, Paris, 1969
P. A. Oskolkov, The uniqueness and global solvability of boundary-value problems for the equations of motion for aqueous solutions of polymers, Institua im. V. A. Steklova an SSSR, Leningrad, vol. 38, 1973, pp. 98–136
P. A. Oskolkov, Solvability in the large of the first boundary-value problem for a quasilinear third-order system pertaining to the motion of a viscous fluid, Instituta im V. A. Steklova Akad. Nauk SSSR, Leningrad, vol. 27, 1972, pp. 145–160
R. Temam, Theory and Numerical Analysis of the Navier-Stokes Equations, North-Holland, Amsterdam, 1977
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Article copyright:
© Copyright 1992
American Mathematical Society
