Scattering for the 3D Gross-Pitaevskii equation

TL;DR

This paper proves scattering results for the 3D Gross-Pitaevskii equation with small initial data, extending understanding of its long-term behavior especially in the radial case.

Contribution

It establishes scattering for small data in the energy space with angular regularity, including the radial case with small energy.

Findings

Proves scattering for small data in the energy space with angular regularity.

Achieves small energy scattering in the radial case.

Extends previous well-posedness results to scattering behavior.

Abstract

We study the Cauchy problem for the 3D Gross-Pitaevskii equation. The global well-posedness in the natural energy space was proved by G\'erard \cite{Gerard}. In this paper we prove scattering for small data in the same space with some additional angular regularity, and in particular in the radial case we obtain small energy scattering.