Blow-up of the non-equivariant 2+1 dimensional wave map

TL;DR

This paper provides numerical evidence that the blow-up phenomenon in 2+1 dimensional wave maps into the 2-sphere remains stable even when the symmetry constraints are explicitly broken, extending understanding beyond symmetric cases.

Contribution

It demonstrates the stability of blow-up in non-equivariant wave maps through numerical experiments, challenging previous assumptions limited to symmetric scenarios.

Findings

Blow-up persists under non-equivariant perturbations.

Numerical simulations confirm stability of blow-up.

Extends understanding of wave map singularities.

Abstract

It has been known for a long time that the equivariant 2+1 wave map into the 2-sphere blows up if the initial data are chosen appropriately. Here, we present numerical evidence for the stability of the blow-up phenomenon under explicit violations of equivariance.