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

✍ Scribed by N. Akroune

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
155 KB
Volume
12
Category
Article
ISSN
0893-9659

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✦ Synopsis

We study the long time behaviour of the solutions to a nonlinear Schr6dinger 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 H 1 (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]). (~

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