Global existence for wave maps with torsion

TL;DR

This paper proves the global existence of smooth solutions for certain wave maps with torsion in 2+1 dimensions, focusing on invariant and equivariant cases with Lie group targets, using geometric frame methods.

Contribution

It establishes global existence results for wave maps with torsion under symmetry reductions and provides a geometric characterization for Lie group targets.

Findings

Global existence of smooth solutions proven for specific reductions

Geometric characterization of wave maps into Lie groups

Applicable to invariant and equivariant wave maps

Abstract

Wave maps (i.e. nonlinear sigma models) with torsion are considered in 2+1 dimensions. Global existence of smooth solutions to the Cauchy problem is proven for certain reductions under a translation group action: invariant wave maps into general targets, and equivariant wave maps into Lie group targets. In the case of Lie group targets (i.e. chiral models), a geometrical characterization of invariant and equivariant wave maps is given in terms of a formulation using frames.