Scattering for the defocusing, cubic nonlinear Schr{ö}dinger equation with initial data in a critical space

Abstract

In this note we prove scattering for a defocusing nonlinear Schr{ö}dinger equation with initial data lying in a critical Besov space. In addition, we obtain polynomial bounds on the scattering size as a function of the critical Besov norm.

References in corpus (4)

• The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher
• The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions
• Global well-posedness and scattering for the radial, defocusing, cubic wave equation with almost sharp initial data
• The radial defocusing nonlinear Schrödinger equation in three space dimensions