# Global well-posedness for the Schr\"odinger map problem with small Besov norm

## TL;DR

This paper proves that the Schr"odinger map problem has a globally well-posed solution when the initial data has a small Besov norm at the critical regularity level.

## Contribution

It establishes global well-posedness for the Schr"odinger map problem under small initial data in a critical Besov space, advancing understanding of the problem's behavior.

## Key findings

- Global well-posedness established for small Besov norm initial data.
- Results apply at critical regularity levels.
- Advances the mathematical theory of Schr"odinger maps.

## Abstract

In this paper we prove a global result for the Schr\"odinger map problem with initial data with small Besov norm at critical regularity.