Sharp global regularity for the 2+1-dimensional equivariant Faddeev model

TL;DR

This paper proves that small initial data in critical Besov spaces lead to global solutions that scatter for the 2+1-dimensional equivariant Faddeev model, a quasilinear generalization of the nonlinear sigma model.

Contribution

It establishes global regularity and scattering results for the equivariant Faddeev model in 2+1 dimensions with small initial data.

Findings

Global solutions exist for small initial data

Solutions scatter as time goes to infinity

The result applies to a quasilinear generalization of the sigma model

Abstract

The aim of this article is to prove that for the 2+1-dimensional equivariant Faddeev model, which is a quasilinear generalization of the corresponding nonlinear sigma model, small initial data in critical Besov spaces evolve into global solutions which scatter.