$L^2$ concentration of blow-up solutions for the mass-critical NLS with inverse-square potential

TL;DR

This paper proves a refined compactness lemma and uses it to demonstrate mass concentration phenomena in solutions to the focusing mass-critical nonlinear Schrödinger equation with an inverse-square potential.

Contribution

It introduces a refined compactness lemma and applies it to establish $L^2$ concentration of blow-up solutions in the presence of an inverse-square potential.

Findings

Established mass concentration for blow-up solutions

Refined compactness lemma for inverse-square potential case

Demonstrated $L^2$ concentration of solutions

Abstract

In this paper, we prove a refined version of a compactness lemma and we use it to establish mass-concentration for the focusing nonlinear Schr\"{o}dinger equation with an inverse-square potential.