Global existence and uniqueness of solutions to the equations of third grade fluids;Remarques sur la limite α → 0 pour les fluides de grade 2

Comptes Rendus Mathematique

Volumn 334, Issue 1, 2002, Pages 83-86

  Iftimie, Dragoş ^a,b  

^a UNIVERSITÉ DE RENNES 1   (France)

^b ECOLE POLYTECHNIQUE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038054011     PISSN: 1631073X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1631-073X(02)02187-8     Document Type: Article

References (17)

1. Busuioc V., On second grade fluids with vanishing viscosity, Portugal. Math. (à paraître).
2. Chemin J.-Y, Méthodes mathématiques en mécanique des fluides, I, Cours de DEA et Preprint Laboratoire d'Analyse Numérique A97004, 1997.
3. Cioranescu D., Girault V., Weak and classical solutions of a family of second grade fluids, Internat. J. Non-Linear Mech. 32 (2) (1997) 317-335.
4. Cioranescu D., Ouazar E.H., Existence and uniqueness for fluids of second grade, in: Nonlinear Partial Differential Equations and Their Applications, Collège de France seminar, Vol. VI (Paris, 1982/1983), Boston, MA, Pitman, 1984, pp. 178-197.
5. Constantin P., Foiaş C., Navier-Stokes Equations, University of Chicago Press, Chicago, 1988.
6. Dunn J.E., Fosdick R.L., Thermodynamics, stability, and boundedness of fluids of complexity 2 and fluids of second grade, Arch. Rational Mech. Anal. 56 (1974) 191-252.
7. Galdi G.P., Grobbelaar-van Dalsen M., Sauer N., Existence and uniqueness of classical solutions of the equations of motion for second-grade fluids, Arch. Rational Mech. Anal. 124 (3) (1993) 221-237.
8. Galdi G.P., Sequeira A., Further existence results for classical solutions of the equations of a second-grade fluid, Arch. Rational Mech. Anal. 128 (4) (1994) 297-312.
9. Iftimie D., Remarques sur la limite α → 0 pour les fluides de grade 2, Nonlinear Partial Differential Equations and Their Applications, Séminaire du Collège de France (à paraître).
10. Leray J., Sur le mouvement d'un liquide visqueux emplissant l'espace, Acta Math. 63 (1934) 193-248.
11. Marsden J.E., Ratiu T.S., Shkoller S., A nonlinear analysis of the averaged Euler equations and a new diffeomorphism group, Geom, Funct. Anal. (à paraître).
12. Marsden J.E., Ratiu T.S., Shkoller S., The geometry and analysis of the averaged Euler equations and a new diffeomorphism group, Geom. Funct. Anal. 10 (3) (2000) 582-599.
13. Oliver M., Shkoller S., The vortex blob method as a second-grade non-Newtonian fluid, Comm. Partial Differential Equations 26 (1-2) (2001) 295-314.
14. Rivlin R.S., Ericksen J.L., Stress-deformation relations for isotropic materials, J. Rational Mech. Anal. 4 (1955) 323-425.
15. Shkoller S., Smooth global Lagrangian flow for the 2D Euler and second-grade fluid equations, Appl. Math. Lett. 14 (5) (2001) 539-543.
16. Taylor M.E., Partial Differential Equations. III, Springer-Verlag, New York, 1997.
17. Temam R., Navier-Stokes Equations, North-Holland, Amsterdam, 1984.