1+2 dimensional radially symmetric wave maps revisit

TL;DR

This paper provides a simplified proof of the global existence of smooth solutions for radially symmetric wave maps from 1+2-dimensional Minkowski space to various Riemannian manifolds, extending previous results to non-compact cases.

Contribution

It introduces an alternative, simpler proof technique for wave maps' global existence and generalizes results to include non-compact target manifolds under certain conditions.

Findings

Proves global existence of smooth solutions for radially symmetric wave maps.

Extends results to non-compact target manifolds with additional assumptions.

Simplifies the proof process compared to previous methods.

Abstract

The author gives an alternative and simple proof of the global existence of smooth solutions to the Cauchy problem for wave maps from the 1+2-dimensional Minkowski space to an arbitrary compact smooth Riemannian manifold without boundary, for arbitrary smooth, radially symmetric data. the author can also treat non-compact manifold under some additional assumptions which generalize the existing ones.