On global attractors for 2D damped driven nonlinear Schr\"odinger equations

TL;DR

This paper proves the existence of global attractors for the 2D damped driven nonlinear Schrödinger equation with almost periodic forcing, using a novel energy equation approach to establish well-posedness and long-term behavior.

Contribution

It introduces a new method leveraging the energy equation to analyze the global attractors for this class of nonlinear Schrödinger equations.

Findings

Established well-posedness of the equation.

Proved existence of a global attractor.

Applied a novel energy equation technique.

Abstract

Well-posedness and global attractor are established for 2D damped driven nonlinear Schr\"odinger equation with almost periodic pumping in a bounded region. The key role is played by a novel application of the energy equation.