The $L^{2}$ sequential convergence of a solution to the mass-critical NLS above the ground state

TL;DR

This paper extends previous results on the convergence of solutions to the mass-critical nonlinear Schrödinger equation, demonstrating $L^{2}$ sequential convergence for non-scattering solutions in higher dimensions without symmetry constraints.

Contribution

It generalizes earlier one-dimensional results to higher dimensions and removes symmetry assumptions for initial data in the analysis of $L^{2}$ convergence.

Findings

Proves $L^{2}$ sequential convergence for non-scattering solutions in dimensions $d \, \geq \, 2$

Extends previous one-dimensional results to higher dimensions

No symmetry assumptions needed for initial data

Abstract

In this paper we generalize a weak sequential result of \cite{fan20182} to a non-scattering solutions in dimension $d \geq 2$. No symmetry assumptions are required for the initial data. We build on a previous result of \cite{dodson20202} for one dimension.