Global Well-Posedness for Cubic NLS with Nonlinear Damping

Antonelli, Paolo; Sparber, Christof

Global Well-Posedness for Cubic NLS with Nonlinear Damping

Type

Article

Authors

Antonelli, Paolo
Sparber, Christof

KAUST Grant Number

KUK-I1-007-43

Date

2010-11-04

Abstract

We study the Cauchy problem for the cubic nonlinear Schrödinger equation, perturbed by (higher order) dissipative nonlinearities. We prove global in-time existence of solutions for general initial data in the energy space. In particular we treat the energy-critical case of a quintic dissipation in three space dimensions. © Taylor & Francis Group, LLC.

Citation

Antonelli P, Sparber C (2010) Global Well-Posedness for Cubic NLS with Nonlinear Damping. Communications in Partial Differential Equations 35: 2310–2328. Available: http://dx.doi.org/10.1080/03605300903540943.

Acknowledgements

The authors want to thank R. Carles for helpful discussions. This publication is based on work supported by Award No. KUK-I1-007-43, funded by the King Abdullah University of Science and Technology (KAUST). The authors thank the Institute for Pure and Applied Mathematics (Los Angeles) for its hospitality and financial support.