Remarques sur la limite $ \mathbf{\alpha \to 0}$ pour les fluides de grade $ \mathrm{2}$

Dragoş Iftimie

doi:10.1016/S1631-073X(02)02187-8

Remarques sur la limite

α \to 0

pour les fluides de grade

2

Dragoş Iftimie ^1,²

¹ IRMAR, Université de Rennes-1, campus de Beaulieu, 35042 Rennes, France
² Centre de mathématiques, École polytechnique, 91128 Palaiseau, France

Comptes Rendus. Mathématique, Volume 334 (2002) no. 1, pp. 83-86.

Résumé
Abstract

On considère la limite α→0 dans l'équation des fluides de grade 2. On montre la convergence faible des solutions vers une solution faible de l'équation de Navier–Stokes, en supposant que les données initiales convergent faiblement dans L².

We consider the limit α→0 for the equation of the second grade fluids. We prove that weak convergence of the solutions to a weak solution of the Navier–Stokes equation holds under the assumption that the initial data weakly converges in L².

Reçu le : 2001-10-24
Accepté le : 2001-10-26
Publié le : 2002-01-01

DOI : 10.1016/S1631-073X(02)02187-8

Affiliations des auteurs :

Dragoş Iftimie ^{1, 2}

¹ IRMAR, Université de Rennes-1, campus de Beaulieu, 35042 Rennes, France
² Centre de mathématiques, École polytechnique, 91128 Palaiseau, France

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Dragoş Iftimie. Remarques sur la limite $ \mathbf{\alpha \to 0}$ pour les fluides de grade $ \mathrm{2}$. Comptes Rendus. Mathématique, Volume 334 (2002) no. 1, pp. 83-86. doi : 10.1016/S1631-073X(02)02187-8. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02187-8/

Bibliographie
Cité par

[1] Busuioc V., On second grade fluids with vanishing viscosity, Portugal. Math. (à paraı̂tre)

[2] Chemin J.-Y., Méthodes mathématiques en mécanique des fluides, I, Cours de DEA et Preprint Laboratoire d'Analyse Numérique A97004, 1997

[3] D. Cioranescu; V. Girault Weak and classical solutions of a family of second grade fluids, Internat. J. Non-Linear Mech., Volume 32 (1997) no. 2, pp. 317-335

[4] D. Cioranescu; E.H. Ouazar Existence and uniqueness for fluids of second grade, Nonlinear Partial Differential Equations and Their Applications, Collège de France seminar, Vol. VI (Paris, 1982/1983), Boston, MA, Pitman, 1984, pp. 178-197

[5] P. Constantin; C. Foiaş Navier–Stokes Equations, University of Chicago Press, Chicago, 1988

[6] J.E. Dunn; R.L. Fosdick Thermodynamics, stability, and boundedness of fluids of complexity 2 and fluids of second grade, Arch. Rational Mech. Anal., Volume 56 (1974), pp. 191-252

[7] G.P. Galdi; M. Grobbelaar-van Dalsen; N. Sauer Existence and uniqueness of classical solutions of the equations of motion for second-grade fluids, Arch. Rational Mech. Anal., Volume 124 (1993) no. 3, pp. 221-237

[8] G.P. Galdi; A. Sequeira Further existence results for classical solutions of the equations of a second-grade fluid, Arch. Rational Mech. Anal., Volume 128 (1994) no. 4, pp. 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 paraı̂tre)

[10] J. Leray Sur le mouvement d'un liquide visqueux emplissant l'espace, Acta Math., Volume 63 (1934), pp. 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 paraı̂tre)

[12] J.E. Marsden; T.S. Ratiu; S. Shkoller The geometry and analysis of the averaged Euler equations and a new diffeomorphism group, Geom. Funct. Anal., Volume 10 (2000) no. 3, pp. 582-599

[13] M. Oliver; S. Shkoller The vortex blob method as a second-grade non-Newtonian fluid, Comm. Partial Differential Equations, Volume 26 (2001) no. 1–2, pp. 295-314

[14] R.S. Rivlin; J.L. Ericksen Stress-deformation relations for isotropic materials, J. Rational Mech. Anal., Volume 4 (1955), pp. 323-425

[15] S. Shkoller Smooth global Lagrangian flow for the 2D Euler and second-grade fluid equations, Appl. Math. Lett., Volume 14 (2001) no. 5, pp. 539-543

[16] M.E. Taylor Partial Differential Equations. III, Springer-Verlag, New York, 1997

[17] R. Temam Navier–Stokes Equations, North-Holland, Amsterdam, 1984

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