Sequential convergence of a solution to the Chern--Simons--Schrodinger equation

TL;DR

This paper proves that certain blowup solutions to the self-dual Chern--Simons--Schrödinger equation converge to a soliton along a subsequence of times, under specific mass conditions.

Contribution

It establishes a sequential convergence result for blowup solutions in the equivariant Chern--Simons--Schrödinger equation, advancing understanding of solution behavior near blowup.

Findings

Blowup solutions with mass less than twice the soliton mass converge to the soliton.

Convergence occurs along a subsequence of times approaching the blowup time.

The result applies to the m-equivariant, self-dual case.

Abstract

In this paper we prove a sequential convergence result for blowup solutions to the $m$-equivariant, self-dual Chern--Simons--Schr{\"o}dinger equation. We show that if $u$ has mass less than twice the mass of the soliton, a blowup solution converges to the soliton along a subsequence of times that converges to the blowup time.