A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2018; you can also visit the original URL.
The file type is application/pdf.
Global attractor and asymptotic smoothing effects for the weakly damped cubic Schrödinger equation in L²(T)
2009
Dynamics of Partial Differential Equations
Preserved Fulltext
We prove that the weakly damped cubic Schrödinger flow in L 2 (T) provides a dynamical system that possesses a global attractor. The proof relies on a sharp study of the behavior of the associated flow-map with respect to the weak L 2 (T)-convergence inspired by [18] . Combining the compactness in L 2 (T) of the attractor with the approach developed in [10], we show that the attractor is actually a compact set of H 2 (T). This asymptotic smoothing effect is optimal in view of the regularity of
doi:10.4310/dpde.2009.v6.n1.a2
fatcat:gh2rd42725d7vl6nvuijak4nbi