Global well-posedness for cubic NLS with nonlinear damping

TL;DR

This paper proves the global existence of solutions for a cubic nonlinear Schrödinger equation with nonlinear damping, including the energy-critical case in three dimensions, extending understanding of dissipative effects on well-posedness.

Contribution

It establishes global well-posedness for the cubic NLS with nonlinear damping, covering the energy-critical quintic dissipation case in three dimensions, which was previously unresolved.

Findings

Global solutions exist for general initial data in the energy space.

The energy-critical case with quintic dissipation in three dimensions is addressed.

The results extend the theory of nonlinear Schrödinger equations with dissipative perturbations.

Abstract

We study the Cauchy problem for the cubic nonlinear Schroedinger 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.