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Regularity of the attractor for a weakly damped nonlinear Schrödinger equation in $\mathbb{R}^2$

Regularity of the attractor for a weakly damped nonlinear Schrödinger equation in $\mathbb{R}^2$

We prove that the global attractor for a weakly damped nonlinear Schrödinger equation in a suitable energy space is in fact included and compact in a more regular energy space.