Dans cette Note, on présente des résultats d'existence et d'unicité pour les équations d'Oseen posées dans des domaines extérieurs de . Le comportement à l'infini des solutions est décrit par l'utilisation des espaces de Sobolev avec poids. L'étude repose sur une théorie , avec .
In this Note, we present existence and uniqueness results for the exterior Oseen problem. In order to control the behavior at infinity of functions, we use as functional framework weighted Sobolev spaces. The results rely on a -theory for .
Accepté le :
Publié le :
@article{CRMATH_2005__341_9_587_0, author = {Amrouche, Ch\'erif and Razafison, Ulrich}, title = {On the existence of solutions in weighted {Sobolev} spaces for the exterior {Oseen} problem}, journal = {Comptes Rendus. Math\'ematique}, pages = {587--592}, publisher = {Elsevier}, volume = {341}, number = {9}, year = {2005}, doi = {10.1016/j.crma.2005.09.007}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2005.09.007/} }
TY - JOUR AU - Amrouche, Chérif AU - Razafison, Ulrich TI - On the existence of solutions in weighted Sobolev spaces for the exterior Oseen problem JO - Comptes Rendus. Mathématique PY - 2005 SP - 587 EP - 592 VL - 341 IS - 9 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2005.09.007/ DO - 10.1016/j.crma.2005.09.007 LA - en ID - CRMATH_2005__341_9_587_0 ER -
%0 Journal Article %A Amrouche, Chérif %A Razafison, Ulrich %T On the existence of solutions in weighted Sobolev spaces for the exterior Oseen problem %J Comptes Rendus. Mathématique %D 2005 %P 587-592 %V 341 %N 9 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2005.09.007/ %R 10.1016/j.crma.2005.09.007 %G en %F CRMATH_2005__341_9_587_0
Amrouche, Chérif; Razafison, Ulrich. On the existence of solutions in weighted Sobolev spaces for the exterior Oseen problem. Comptes Rendus. Mathématique, Tome 341 (2005) no. 9, pp. 587-592. doi : 10.1016/j.crma.2005.09.007. http://archive.numdam.org/articles/10.1016/j.crma.2005.09.007/
[1] C. Amrouche, U. Razafison, The stationary Oseen equations in . An approach in weighted Sobolev spaces, Preprint no 2004/09, Université de Pau et des Pays de l'Adour (2004); J. Math. Fluid Mech., submitted for publication
[2] C. Amrouche, U. Razafison, On the Oseen problem in three-dimensional exterior domains, Preprint no 2005/03, Université de Pau et des Pays de l'Adour (2005)
[3] Dirichlet and Neumann exterior problems for the n-dimensional Laplace operator: an approach in weighted Sobolev spaces, J. Math. Pures. Appl., Volume 73 (1994) no. 1, pp. 579-606
[4] The stationary exterior 3D-problem of Oseen and Navier–Stokes equations in anisotropically weighted Sobolev spaces, Math. Z., Volume 211 (1992) no. 3, pp. 409-447
[5] R. Farwig, H. Sohr, Weighted estimates for the Oseen equations and the Navier–Stokes equations in exterior domains, in: Theory of the Navier–Stokes Equations, Ser. Adv. Math. Sci., vol. 47, 1998, pp. 11–30
[6] On the exterior stationary problem for the Navier–Stokes equations, and associated perturbation problems, Arch. Rational. Mech. Anal., Volume 19 (1965), pp. 363-406
[7] On the Oseen boundary value problem in exterior domains, (Oberwolfach, 1991) (Lecture Notes in Math.), Springer-Verlag, Berlin (1992), pp. 111-131
[8] An Introduction to the Mathematical Theory of the Navier–Stokes Equations, vol. I, Springer Tracts in Natural Philosophy, vol. 38, Springer-Verlag, Berlin, 1994
Cité par Sources :