Small data global regularity for half-wave maps

TL;DR

This paper proves that small initial data in Besov spaces lead to global regularity for the half-wave maps problem targeting the sphere in high dimensions.

Contribution

It establishes global regularity results for the half-wave maps problem with small critical data in Besov spaces in high dimensions.

Findings

Global regularity for small data in high dimensions

Use of Besov spaces for initial data analysis

Extension of regularity results to half-wave maps

Abstract

We formulate the half-wave maps problem with target $S^2$ and prove global regularity in sufficiently high spatial dimensions for a class of small critical data in Besov spaces.