Blowup stability of wave maps without symmetry

TL;DR

This paper proves the asymptotic stability of a self-similar blowup solution for wave maps from Minkowski space into the sphere, without symmetry assumptions, using a fully rigorous analytical approach.

Contribution

It establishes the first rigorous proof of stability for blowup solutions in wave maps without symmetry constraints.

Findings

Self-similar blowup solution exists for wave maps into the sphere.

The blowup solution is asymptotically stable under small perturbations.

The proof is fully rigorous and does not rely on numerical methods.

Abstract

We study wave maps from $(1+d)$-dimensional Minkowski space into the $d$-sphere without any symmetry assumptions. There exists an explicit self-similar blowup solution and we prove that this solution is asymptotically stable under small perturbations of the initial data. The proof is fully rigorous and requires no numerical input whatsoever.