Global attractor for weakly damped Nonlinear Schrödinger equations in $L^2(\R)$

Olivier Goubet (1) , Luc Molinet (2)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée
2 LAGA - Laboratoire Analyse, Géométrie et Applications

We prove that the weakly damped nonlinear Schrödinger flow in $L^2(\mathbb{R})$ provides a dynamical system which possesses a global attractor. The proof relies on the continuity of the Schrödinger flow for the weak topology in $L^2(\R)$.

Domaines: Equations aux dérivées partielles [math.AP]

Olivier Goubet, Luc Molinet. Global attractor for weakly damped Nonlinear Schrödinger equations in $L^2(\R)$. Nonlinear Analysis: Theory, Methods and Applications, 2009, 71, pp.317-320. ⟨hal-00421278⟩