[Un attracteur pullback pour un système de Navier–Stokes bidimensionel non autonome dans un domaine non borné]
Dans cette Note, on présente d'abord la notion de compacité asymptotique pullback. On établit ensuite un résultat d'existence d'un attracteur pullback pour un système dynamique non autonome, sous les hypothèses de compacité asymptotique pullback et d'existence d'une famille d'ensembles absorbants au sens pullback. On prouve finalement l'existence d'un attracteur pullback pour un système de Navier–Stokes bidimensionel non autonome dans un domaine non borné, une situation dans laquelle, étant donnée la généralité du terme non autonome, la théorie des attracteurs uniformes ne peut pas être appliquée.
In this Note we first introduce the concept of pullback asymptotic compactness. Next, we establish a result ensuring the existence of a pullback attractor for a non-autonomous dynamical system under the general assumptions of pullback asymptotic compactness and the existence of a pullback absorbing family of sets. Finally, we prove the existence of a pullback attractor for a non-autonomous 2D Navier–Stokes model in an unbounded domain, a case in which the theory of uniform attractors does not work since the non-autonomous term is quite general.
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@article{CRMATH_2006__342_4_263_0,
author = {Caraballo, Tom\'as and {\L}ukaszewicz, Grzegorz and Real, Jos\'e},
title = {Pullback attractors for non-autonomous {2D-Navier{\textendash}Stokes} equations in some unbounded domains},
journal = {Comptes Rendus. Math\'ematique},
pages = {263--268},
publisher = {Elsevier},
volume = {342},
number = {4},
year = {2006},
doi = {10.1016/j.crma.2005.12.015},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2005.12.015/}
}
TY - JOUR AU - Caraballo, Tomás AU - Łukaszewicz, Grzegorz AU - Real, José TI - Pullback attractors for non-autonomous 2D-Navier–Stokes equations in some unbounded domains JO - Comptes Rendus. Mathématique PY - 2006 SP - 263 EP - 268 VL - 342 IS - 4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2005.12.015/ DO - 10.1016/j.crma.2005.12.015 LA - en ID - CRMATH_2006__342_4_263_0 ER -
%0 Journal Article %A Caraballo, Tomás %A Łukaszewicz, Grzegorz %A Real, José %T Pullback attractors for non-autonomous 2D-Navier–Stokes equations in some unbounded domains %J Comptes Rendus. Mathématique %D 2006 %P 263-268 %V 342 %N 4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2005.12.015/ %R 10.1016/j.crma.2005.12.015 %G en %F CRMATH_2006__342_4_263_0
Caraballo, Tomás; Łukaszewicz, Grzegorz; Real, José. Pullback attractors for non-autonomous 2D-Navier–Stokes equations in some unbounded domains. Comptes Rendus. Mathématique, Tome 342 (2006) no. 4, pp. 263-268. doi : 10.1016/j.crma.2005.12.015. http://www.numdam.org/articles/10.1016/j.crma.2005.12.015/
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