Singularity Formation in 2+1 Wave Maps

TL;DR

This paper provides numerical evidence that finite-time singularities can develop in 2+1 wave maps with certain initial conditions, highlighting critical behaviors in nonlinear wave equations.

Contribution

It demonstrates for the first time through numerical simulations that singularities form in finite time in 2+1 wave maps with spherically equivariant initial data of sufficient energy.

Findings

Singularities form in finite time during evolution.

Finite energy initial data can lead to singularity formation.

Numerical evidence supports theoretical predictions.

Abstract

We present numerical evidence that singularities form in finite time during the evolution of 2+1 wave maps from spherically equivariant initial data of sufficient energy.