Regularity of the attractor for a weakly damped nonlinear Schrödinger equation on R

AbstractWe study the long time behaviour of the solutions to a nonlinear Schrödinger equation, in presence of a damping term, and a forcing term, when the space variable x varies over R. We show that the long time behaviour is described by an attractor which captures all the trajectories in H1(R). Our main result is concerned with the asymptotic smoothing effect for the equations. In other words, we prove that the attractor is included and compact in H2(R), generalizing results proven in [1] in the compact (bounded) case (see also [2])

Determination numerique de la mesure locale limite d'un ensemble de JULIA

CNRS RS 17660 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueSIGLEFRFranc