Large data global regularity for the $2+1$-dimensional equivariant Faddeev model

TL;DR

This paper proves that the 2+1-dimensional equivariant Faddeev model remains globally regular for large initial data in certain Sobolev spaces, extending understanding of its well-posedness.

Contribution

It establishes large data global regularity for the equivariant Faddeev model in 2+1 dimensions for initial data in Sobolev spaces with regularity s>3.

Findings

Global regularity holds for large data in H^s×H^{s-1} with s>3

The result applies to the equivariant case of the Faddeev model

Extends previous small data results to large data regime

Abstract

This article addresses the large data global regularity for the equivariant case of the $2+1$-dimensional Faddeev model and shows that it holds true for initial data in $H^s\times H^{s-1}(\mathbb{R}^2)$ with $s>3$.