# Global Nonlinear Stability of Geodesic Solutions of Evolutionary Faddeev Model

## TL;DR

This paper proves the global nonlinear stability of geodesic solutions in the evolutionary Faddeev model, which describes maps from Minkowski space to the sphere, demonstrating the stability of large, nontrivial solutions.

## Contribution

It establishes the first rigorous proof of global nonlinear stability for geodesic solutions in the evolutionary Faddeev model.

## Key findings

- Geodesic solutions are globally nonlinearly stable.
- Large, nontrivial solutions remain stable over time.
- The stability result applies to maps from Minkowski space to the sphere.

## Abstract

In this paper, for evolutionary Faddeev model corresponding to maps from the Minkowski space $\mathbb{R}^{1+n}$ to the unit sphere $\mathbb{S}^2$, we show the global nonlinear stability of geodesic solutions, which are a kind of nontrivial and large solutions.