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

Abstract

In this paper, we prove that the cubic nonlinear Schrödinger 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 Schrödinger equation setting.

Detailed proof of claim 5.5 added

References in corpus (2)

• Fractional Quantum Mechanics
• I-method for Defocusing, Energy-Subcritical Non-linear Wave Equation

Cited by in corpus (1)

• Global well-posedness and long-time behavior of the fractional NLS