On collapse of wave maps

TL;DR

This paper derives a universal collapse law for degree 1 equivariant wave maps from 2+1 Minkowski space to the 2-sphere, using a nonlinear transformation and numerical validation.

Contribution

It introduces a new nonlinear transformation to analyze wave map collapse and confirms the theoretical predictions with numerical simulations.

Findings

Derived the universal collapse law for wave maps.

Validated the collapse law through numerical simulations.

Provided a new analytical framework for wave map singularity analysis.

Abstract

We derive the universal collapse law of degree 1 equivariant wave maps (solutions of the sigma-model) from the 2+1 Minkowski space-time,to the 2-sphere. To this end we introduce a nonlinear transformation from original variables to blowup ones. Our formal derivations are confirmed by numerical simulations.