Regularity of the attractor for Schrödinger equation Original Research Article

We prove that the global attractor for a weakly damped nonlinear Schrödinger equation is smooth, i.e., it is made of smooth functions when the forcing term is smooth. Our study relies on a new approach that works for dispersive equations that are weakly dissipative, i.e., for equations for which the damping is on the low-order term.