Bootstrapped Morawetz Estimates And Resonant Decomposition For Low Regularity Global Solutions Of Cubic NLS On R^{2}

TL;DR

This paper establishes global solutions for the cubic nonlinear Schrödinger equation on R^2 with low regularity initial data, using advanced analytical techniques to extend well-posedness results.

Contribution

It introduces novel bootstrapped Morawetz estimates and resonant decomposition methods to achieve global well-posedness for s > 1/3, improving previous regularity thresholds.

Findings

Global well-posedness for s > 1/3

Novel use of Morawetz estimates and resonant decomposition

Extension of low regularity solutions for cubic NLS

Abstract

We prove global well-posedness for the L^{2}-critical cubic defocusing nonlinear Schr\"odinger equation on R^{2} with data u_{0} \in H^{s}(R^{2}) for s > {1/3}.