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

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.