# A Liouville theorem for the Chern--Simons--Schr{\"o}dinger equation

## TL;DR

This paper proves a Liouville theorem for the Chern--Simons--Schr{"o}dinger equation, supporting the soliton resolution conjecture for certain initial data, and extends understanding of the equation's solutions.

## Contribution

The paper establishes a Liouville theorem for the Chern--Simons--Schr{"o}dinger equation, contributing to the theoretical understanding of its solution behavior.

## Key findings

- Liouville theorem proven for the equation
- Supports soliton resolution conjecture in unweighted spaces
- Extends previous results in weighted spaces

## Abstract

In this paper we prove a Liouville theorem for the Chern--Simons--Schr{\"o}dinger equation. This result is consistent with the soliton resolution conjecture for initial data that does not lie in a weighted space. See [KKO22] for the soliton resolution result in a weighted space.