Global well-posedness for the cubic fractional NLS on the unit disk

TL;DR

This paper establishes global well-posedness for the cubic fractional nonlinear Schrödinger equation on the unit disk for specific radial initial data below the energy space, using an extended I-method.

Contribution

It extends the I-method to fractional NLS on the unit disk, proving global well-posedness for a new class of initial data.

Findings

Global well-posedness for fractional NLS on the unit disk

Extension of the I-method to fractional Laplacian setting

Well-posedness for data below the energy space

Abstract

In this paper, we prove that the cubic nonlinear Schr\"odinger equation with the fractional Laplacian on the unit disk is globally well-posed for certain radial initial data below the energy space. The result is proved by extending the I-method in the fractional nonlinear Schr\"odinger equation setting.