Small data global regularity for half-wave maps in $n = 4$ dimensions

TL;DR

This paper proves global well-posedness for small initial data in a critical Besov space for the half-wave maps problem in four spatial dimensions, extending results known for wave maps.

Contribution

It establishes the first global regularity result for half-wave maps in four dimensions with small data in a critical Besov space, paralleling wave map results.

Findings

Global well-posedness for small data in critical Besov space

Extension of wave map regularity results to half-wave maps

Applicable in four spatial dimensions

Abstract

We prove that the half-wave maps problem on $\mathbb{R}^{4+1}$ with target $S^2$ is globally well-posed for smooth initial data which are small in the critical $l^1$ based Besov space. This is a formal analogue of the result for wave maps by Tataru.