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September  2009, 8(5): 1555-1575. doi: 10.3934/cpaa.2009.8.1555

## Global attractor for the Davey-Stewartson system on $\mathbb R^2$

 1 Universite de Picardie Jules Verne, LAMFA UMR 7352, 33 rue Saint-Leu, 80039 Amiens cedex 2 Laboratoire Paul Painlev, UFR de Mathmatiques Pures et Appliques, Universit des Sciences et Technologies de Lille, 59655 Villeneuve d’Ascq, Equipe SIMPAF INRIA Centre de Recherche Lille Nord Eur, France

Received  August 2008 Revised  January 2009 Published  April 2009

We prove that the weakly damped Davey-Stewartson system (DS), considered as an infinite-dimensional dynamical system in $H^1(\mathbb R^2)$, has a compact global attractor that is actually a compact subset of $H^2(\mathbb R^2)$.
Citation: Olivier Goubet, Manal Hussein. Global attractor for the Davey-Stewartson system on $\mathbb R^2$. Communications on Pure & Applied Analysis, 2009, 8 (5) : 1555-1575. doi: 10.3934/cpaa.2009.8.1555
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