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

Abstract

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 $L^2(\mathbb{R})$.