Optimal blowup stability for supercritical wave maps

TL;DR

This paper proves the stability of a known self-similar wave map in a supercritical setting, demonstrating that small perturbations in the critical Sobolev space do not destabilize it.

Contribution

It establishes the first rigorous stability result for a supercritical wave map with explicit self-similar solutions.

Findings

Self-similar wave map is stable under small critical Sobolev perturbations.

The stability proof applies to corotational wave maps from 5D Minkowski space.

The result advances understanding of supercritical wave map dynamics.

Abstract

We study corotational wave maps from $(1+4)$-dimensional Minkowski space into the $4$-sphere. We prove the stability of an explicitly known self-similar wave map under perturbations that are small in the critical Sobolev space.