Comptes Rendus
no. 13-14
Partial Differential Equations/Probability Theory
Asymptotic behavior of solutions of stochastic evolution equations for second grade fluids
[Comportement asymptotique des solutions d'équations d'évolution stochastiques des fluides de grade deux]

Présenté par : Pierre-Louis Lions

Paul André Razafimandimby1 ; Mamadou Sango1
1 Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa
Comptes Rendus. Mathématique, Volume 348 (2010) no. 13-14, pp. 787-790.

Dans cette Note nous montrons que, sous des hypothèses appropriées sur les données, on peut construire une suite de solutions fortes des équations stochastiques pour les fluides de grade deux qui convergent vers les solutions fortes probabilistes des équations stochastiques de Navier–Stokes quand le module de contrainte α tend vers zéro.

In this Note we show that under suitable conditions on the data we can construct a sequence of solutions of the stochastic second grade fluid that converges to the probabilistic strong solution of the stochastic Navier–Stokes equations when the stress modulus α tends to zero.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.05.001
Paul André Razafimandimby 1 ; Mamadou Sango 1

1 Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa 
@article{CRMATH_2010__348_13-14_787_0,
     author = {Paul Andr\'e Razafimandimby and Mamadou Sango},
     title = {Asymptotic behavior of solutions of stochastic evolution equations for second grade fluids},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {787--790},
     publisher = {Elsevier},
     volume = {348},
     number = {13-14},
     year = {2010},
     doi = {10.1016/j.crma.2010.05.001},
     language = {en},
}
TY  - JOUR
AU  - Paul André Razafimandimby
AU  - Mamadou Sango
TI  - Asymptotic behavior of solutions of stochastic evolution equations for second grade fluids
JO  - Comptes Rendus. Mathématique
PY  - 2010
SP  - 787
EP  - 790
VL  - 348
IS  - 13-14
PB  - Elsevier
DO  - 10.1016/j.crma.2010.05.001
LA  - en
ID  - CRMATH_2010__348_13-14_787_0
ER  - 
%0 Journal Article
%A Paul André Razafimandimby
%A Mamadou Sango
%T Asymptotic behavior of solutions of stochastic evolution equations for second grade fluids
%J Comptes Rendus. Mathématique
%D 2010
%P 787-790
%V 348
%N 13-14
%I Elsevier
%R 10.1016/j.crma.2010.05.001
%G en
%F CRMATH_2010__348_13-14_787_0
Paul André Razafimandimby; Mamadou Sango. Asymptotic behavior of solutions of stochastic evolution equations for second grade fluids. Comptes Rendus. Mathématique, Volume 348 (2010) no. 13-14, pp. 787-790. doi : 10.1016/j.crma.2010.05.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.05.001/

[1] A. Bensoussan Stochastic Navier–Stokes equations, Acta Applicandae Mathematicae, Volume 38 (1995), pp. 267-304

[2] A. Bensoussan; R. Temam Equations Stochastiques du Type Navier–Stokes, Journal of Functional Analysis, Volume 13 (1973), pp. 195-222

[3] A.V. Busuioc On second grade fluids with vanishing viscosity, C. R. Acad. Sci. Paris, Ser. I, Volume 328 (1999) no. 12, pp. 1241-1246

[4] J.-Y. Chemin, Perfect Incompressible Fluids, Clarendon-Oxford University Press

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

[6] D. Cioranescu; E.H. Ouazar Existence and uniqueness for fluids of second grade, College de France Seminar Pitman, Volume 109 (1984), pp. 178-197

[7] J.E. Dunn; R.L. Fosdick Thermodynamics, stability and boundedness of fluids of complexity two and fluids of second grade, Arch. Rat. Mech. Anal., Volume 56 (1974) no. 3, pp. 191-252

[8] D. Iftimie Remarques sur la limite α→0 pour les fluides de grade 2, C. R. Acad. Sci. Paris, Ser. I, Volume 334 (2002) no. 1, pp. 83-86

[9] J.-L. Menaldi; S.S. Sritharan Stochastic 2-D Navier–Stokes equations, Appl. Math. Optim., Volume 46 (2002), pp. 31-53

[10] W. Noll; C. Truesdell The Nonlinear Field Theory of Mechanics, Handbuch der Physik, vol. III, Springer-Verlag, Berlin, 1975

[11] P.A. Razafimandimby, M. Sango, Weak solutions of a stochastic model for two-dimensional second grade fluids, Boundary Value Problems, vol. 2010, Article ID 636140, p. 47

[12] P.A. Razafimandimby; M. Sango Strong solution for a stochastic model of two-dimensional second grade fluids: Existence, uniqueness and stability http://users.aims.ac.za/~paul/publications.html (Preprint:)

[13] M. Sango Magnetohydrodynamic turbulent flows: Existence results, Physica D: Nonlinear Phenomena, Volume 239 (2010) no. 12, pp. 912-923

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

Neumann problem for a quasilinear elliptic equation in a varying domain

Mamadou Sango

C. R. Math (2006)