On scattering for the quintic defocusing nonlinear Schr\"odinger equation on \R \times \T^2

TL;DR

This paper studies the large data scattering problem for the energy- and mass-critical quintic nonlinear Schrödinger equation on a mixed Euclidean-torus space, introducing a new large scale profile to understand solution behavior.

Contribution

It introduces a novel large scale profile to analyze the asymptotic behavior of solutions to the critical NLS on  imes \u00f6^2, advancing understanding of scattering in this setting.

Findings

Identification of a new large scale profile controlling asymptotic behavior

Establishment of scattering results for large data in the critical setting

Development of analytical tools for mixed Euclidean-torus geometries

Abstract

We consider the problem of large data scattering for the quintic nonlinear Schr\"odinger equation on $\R \times \T^2$. This equation is critical both at the level of energy and mass. Most notably, we exhibit a new type of profile (a "large scale profile") that controls the asymptotic behavior of the solutions.